LOADING . . .

CBSE Solutions for Class 11 English

GSEB std 10 science solution for Gujarati check Subject Chapters Wise::

Evalute the following : (5+√2i)/(1-√2i)

Hide | Show

જવાબ : 1 + 2√2i


Evalute the following :  (11-4i-21+i)(1-4i5+i)

Hide | Show

જવાબ : 307/442 + 599/442 i


Evalute the following : 3-4i/(4-2i)(1+i)

Hide | Show

જવાબ : ¼ - ¾ i


Evalute the following : (1+2i)-3

Hide | Show

જવાબ : −11/125 + 2i/125


Evalute the following : (1-i)3/1-i3

Hide | Show

જવાબ : -2+0i


Find the value of the following : i457

Hide | Show

જવાબ : i


Find the value of the following : i528

Hide | Show

જવાબ : 1


Find the value of the following : 1/i58

Hide | Show

જવાબ : -1


Find the value of the following : i37+ 1/i67

Hide | Show

જવાબ : 2i


Find the value of the following : (i41 + 1/i257)9

Hide | Show

જવાબ : 0


Find the value of the following : (i77 + i70 + i87 + i414 )3

Hide | Show

જવાબ : -8


Find the value of the following :  30 + i40 + i60

Hide | Show

જવાબ : 1


Find the value of the following :  i49+i68+i89+i110

Hide | Show

જવાબ : 2i


Evalute the following : (1+i)(1+2i)

Hide | Show

જવાબ : −1+3i


Evalute the following : (3+2i)/(-2+i)

Hide | Show

જવાબ : −4/5 – 7/5 i


Evalute the following : 1/(2+i)2

Hide | Show

જવાબ : 3/25 – 4/25 i


Evalute the following :  (1-i)/(1+i)

Hide | Show

જવાબ : -i


Evalute the following :  (2+i)3/2+3i

Hide | Show

જવાબ : 37/13 + 16/13 i


Evalute the following :  (1+i)(1+√3i)/(1-i)

Hide | Show

જવાબ : −√3+i


Evalute the following : (2+3i)/(4+5i)

Hide | Show

જવાબ : 23/41 + 2/41 i


Find the values of x and y :  (1+i)(x+iy)=2-5i

Hide | Show

જવાબ : x=−32 and y=−72


Find the values of x and y :  [(1+i)x-2i]/(3+i) + [(2-3i)y+i]/(3-i)

Hide | Show

જવાબ : x=3 and y=−1


Find the values of x and y :  (3x-2iy)(2+i)2=10(1+i)

Hide | Show

જવાબ : x=14/15 y=15


Find the values of x and y :  (x+iy)(2-3i)=4+i

Hide | Show

જવાબ : x=5/13 and y=14/13


Find the conjugates of  complex numbers :  (3-2i)(2+3i)/(1+2i)(2-i)

Hide | Show

જવાબ : (63+16i)/25


Find the conjugates of  complex numbers :  (1+i)(2+i)/(3+i)

Hide | Show

જવાબ : 3−4i/5


Find the conjugates of  complex numbers :  (3-i)2/2+i

Hide | Show

જવાબ : 2+4i


Find the conjugates of  complex numbers :  1/1+i

Hide | Show

જવાબ : (63+16i)/25


Find the conjugates of  complex numbers :  1/(3+5i)

Hide | Show

જવાબ : (3+5i)/34


Find the conjugates of  complex numbers :  4 − 5 i

Hide | Show

જવાબ : 4+5i


Find the multiplicative inverse of the complex numbers : √5+3i

Hide | Show

જવાબ : √5/14 – 3/14


Find the multiplicative inverse of the complex numbers : 4 − 3i

Hide | Show

જવાબ : 4/25 + 3/25i


Find the multiplicative inverse of the complex numbers : (1+i√3)2

Hide | Show

જવાબ : −1/8 − 3/√8 i


Find the multiplicative inverse of the complex numbers : 1 − i

Hide | Show

જવાબ : ½ + ½ i


True and False : Region represented by |z+7i|≤5 is On or inside the circle having centre (0, -7) and radius 5 units

Hide | Show

જવાબ : True


True and False : Region represented by |z+7|≤5 is On or inside the circle having centre (–7, 0) and radius 5 units

Hide | Show

જવાબ : True


True and False : The cube root of the unit when represented on the Argand plane form the vertices of an
equilateral triangle

Hide | Show

જવાબ : True


True and False : If three complex numbers are in A.P, then they lie on a circle in the complex plane

Hide | Show

જવાબ : False


Solve the following  :  i6

Hide | Show

જવાબ : -1


Solve the following  :  i5

Hide | Show

જવાબ : i


Solve the following  :  i-2

Hide | Show

જવાબ : -1


Solve the following  :   i-3

Hide | Show

જવાબ : -i


Solve the following  :  i-4

Hide | Show

જવાબ : 1


Solve the following  :   i-5

Hide | Show

જવાબ : i


Solve the following  :   i-6

Hide | Show

જવાબ : -1


Solve the following  :  i-7

Hide | Show

જવાબ : -i


Solve the following  :  i2

Hide | Show

જવાબ : -1


Solve the following  :  i2

Hide | Show

જવાબ : -1


Solve the following  :  i3

Hide | Show

જવાબ : -i


Solve the following  :  i4

Hide | Show

જવાબ : 1


Find the values of i8i10 + i15

 

Hide | Show

જવાબ : i8 + i10 + i15 =i4 +  i4×2+2 + i4×3+3 =(i4)2 + {(i4)2×i2} + {(i4)3×i3} =1+i2+i3 

[i4=1] =1−1−i

[i2=−1, i3=−i ]   =−i


Find the values of i6 + i3 + i4 + i5

Hide | Show

જવાબ : i6 + i3 + i4 + i5 = −1 –I +1 + i           [i2=−1, i3=−i and i4=1]


Find the values of i44 + i80 + i120

Hide | Show

જવાબ : i44 + i80 +i120 = i4×11 + i4×20 + i4×30 = {(i4)11} + {(i4)20} + {(i4)30} = 1+1+1            

[i4=1]=3 


Find the values of  i48 + i68 + i89 + i114

 

Hide | Show

જવાબ : i48+i68+i89+i114 =i4×12 + i4×17 + i4×22+1 + i4×28+2 ={(i4)12} + {(i4)17} + {(i4)22×i} + {(i4)28×i2} =1+1+i+i2                    [i4=1] =i+2−1                       [i2=−1]   = i+1


Show that i9 + i20 + i34 is a real number.

Hide | Show

જવાબ : I9 + i20 + i34 = i4×2+1 + i4×5 + i4×8+2 = [(i4)2×i] +(i4)5 + [(i4)8×i2] = i+1+i2                             ( i4=1)

= i + 1 −1                               ( i2=−1)

=i

This isn’t  a real number.


Show that i9 + i24 is a real number.

Hide | Show

જવાબ : I9 + i24  = i4×2+1 + i4×6 = [(i4)2×i] +(i4)6  = i+1                             ( i4=1)

= i + 1                   

This isn’t a real number.


Show that i14 + i20 is a real number.

Hide | Show

જવાબ : i14 + i20  = i4×3+2 + i4×5 = [(i4)3×i2] +(i4)5  = i2+1                             ( i4=1)

= −1 + 1                               ( i2=−1)

=0

This is a real number.


Show that i10 + i24 + i30 is a real number.

Hide | Show

જવાબ : i10 + i24 + i30 = i4×2+2 + i4×6 + i4×7+2 = [(i4)2×i2] +(i4)6 + [(i4)7×i2] = i2+1+i2                             ( i4=1)

= −1 + 1 −1                               ( i2=−1)

=-1

This is a real number.


If [(1-i)/(1+i)]98 = a+ib, find (ab).

Hide | Show

જવાબ : (1-i)/(1+i) = (1-i)/(1+i) × (1-i)/(1-i)         

=(1-i)2/12-i2         

=12+i2-2i/(1+1)                  [ i2=-1]               

=(1-1-2i)/2         

=-2i/2         

=-i                            ....(1)

It is given that,
 [(1-i)/(1+i)]102=a+ib

(-i)102 = a+ib             [From (1)]

i4×24+2 = a+ib

-1 + 0i =a+ib                [ i4=1]

a=-1 and b=0

Thus, (ab) = (-1, 0).


If [(1-i)/(1+i)]96 = a+ib, find (ab).

Hide | Show

જવાબ : (1-i)/(1+i) = (1-i)/(1+i) × (1-i)/(1-i)         

=(1-i)2/12-i2         

=12+i2-2i/(1+1)                  [ i2=-1]               

=(1-1-2i)/2         

=-2i/2         

=-i                            ....(1)

It is given that,
 [(1-i)/(1+i)]96=a+ib

(-i)96 = a+ib             [From (1)]

i4×24 = a+ib

1 + 0i =a+ib                [ i4=1]

a=1 and b=0

Thus, (ab) = (1, 0).


Find the values of i4 + i10 + i15

Hide | Show

જવાબ : i4 + i10 + i15 =i4 +  i4×2+2 + i4×3+3 =i4+{(i4)2×i2} + {(i4)3×i3} =1+i2+i3                  [i4=1] =1−1−i                     [i2=−1, i3=−i ]   =−i


Find the values of i2 + i3 + i4 + i5

Hide | Show

જવાબ : i2 + i3 + i4 + i5 = −1 –I +1 + i           [i2=−1, i3=−i and i4=1]

=0 


Find the values of i40 + i80 + i120

Hide | Show

જવાબ : i40 + i80 +i120 = i4×10 + i4×20 + i4×30 = {(i4)10} + {(i4)20} + {(i4)30} = 1+1+1             [i4=1]=3


Find the values of  i48 + i68 + i89 + i110

 

Hide | Show

જવાબ : i48+i68+i89+i110 =i4×12 + i4×17 + i4×22+1 + i4×27+2 ={(i4)12} + {(i4)17} + {(i4)22×i} + {(i4)27×i2} =1+1+i+i2                    [i4=1] =i+2−1                       [i2=−1]   = i+1


Show that i9 + i20 + i30 is a real number.

Hide | Show

જવાબ : I9 + i20 + i30 = i4×2+1 + i4×5 + i4×7+2 = [(i4)2×i] +(i4)5 + [(i4)7×i2] = i+1+i2                             ( i4=1)

= i + 1 −1                               ( i2=−1)

=i

This isn’t  a real number.


Show that i9 + i20 is a real number.

Hide | Show

જવાબ : I9 + i20  = i4×2+1 + i4×5 = [(i4)2×i] +(i4)5  = i+1                             ( i4=1)

= i + 1                   

This isn’t a real number.


Show that i10 + i20 is a real number.

Hide | Show

જવાબ : i10 + i20  = i4×2+2 + i4×5 = [(i4)2×i2] +(i4)5  = i2+1                             ( i4=1)

= −1 + 1                               ( i2=−1)

=0

This is a real number.


Show that i10 + i20 + i30 is a real number.

Hide | Show

જવાબ : i10 + i20 + i30 = i4×2+2 + i4×5 + i4×7+2 = [(i4)2×i2] +(i4)5 + [(i4)7×i2] = i2+1+i2                             ( i4=1)

= −1 + 1 −1                               ( i2=−1)

=-1

This is a real number.


If [(1-i)/(1+i)]102 = a+ib, find (ab).

Hide | Show

જવાબ : (1-i)/(1+i) = (1-i)/(1+i) × (1-i)/(1-i)         

=(1-i)2/12-i2         

=12+i2-2i/(1+1)                  [ i2=-1]               

=(1-1-2i)/2         

=-2i/2         

=-i                            ....(1)

It is given that,
 [(1-i)/(1+i)]102=a+ib

(-i)102 = a+ib             [From (1)]

i4×25+2 = a+ib

-1 + 0i =a+ib                [ i4=1]

a=-1 and b=0

Thus, (ab) = (-1, 0).


If [(1-i)/(1+i)]104 = a+ib, find (ab).

Hide | Show

જવાબ : (1-i)/(1+i) = (1-i)/(1+i) × (1-i)/(1-i)         

=(1-i)2/12-i2         

=12+i2-2i/(1+1)                  [ i2=-1]               

=(1-1-2i)/2         

=-2i/2         

=-i                            ....(1)

It is given that,
 [(1-i)/(1+i)]104=a+ib

(-i)104 = a+ib             [From (1)]

i4×26 = a+ib

1 + 0i =a+ib                [ i4=1]

a=1 and b=0

Thus, (ab) = (1, 0).


There are No Content Availble For this Chapter

1

√64

A

-8

2

√-64

B

8

3

-√64

C

8i

Hide | Show

જવાબ :

1-B,2-C,3-A

1

√49

A

-7

2

√-49

B

7i

3

-√49

C

7

Hide | Show

જવાબ :

1-C, 2-B, 3-A

1

√25

A

6

2

√-25

B

6i

3

√-36

C

5i

4

√36

D

5

Hide | Show

જવાબ :

1-D, 2-A, 3-B, 4-C

1

√196

A

-16

2

√-196

B

16i

3

-√196

C

16

Hide | Show

જવાબ :

1-C, 2-A, 3-B

1

√4

A

12

2

√-4

B

12i

3

√-144

C

2i

4

√144

D

2

Hide | Show

જવાબ :

1-D, 2-C, 3-B, 4-A

1

I9

A

1

2

I10

B

-i

3

I11

C

i

4

I12

D

-1

Hide | Show

જવાબ :

1-C, 2-D, 3-B, 4-A

1

I6

A

-1

2

I7

B

-i

3

I8

C

1

Hide | Show

જવાબ :

1-C, 2-A, 3-B

1

I-2

A

i

2

i-1

B

-1

3

I-3

C

1

4

i-4

D

-i

Hide | Show

જવાબ :

1-B, 2-C, 3-D, 4-A

1

i2

A

1

2

I3

B

I

3

I4

C

-1

4

I5

D

-i

Hide | Show

જવાબ :

1-C, 2-D, 3-A, 4-B

1

i20

A

-i

2

i21

B

-1

3

i22

C

I

4

i23

D

1

Hide | Show

જવાબ :

1-D, 2-C, 3-B, 4-A

Download PDF

Take a Test

Choose your Test :

Complex Numbers and Quardratic Equations

-.

આ પ્રકરણને લગતા વિવિધ એનિમેશન વિડીયો, હેતુલક્ષી પ્રશ્નો, ટૂંકા પ્રશ્નો, લાંબા પ્રશ્નો, પરિક્ષામાં પુછાઈ ગયેલા પ્રશ્નો તેમજ પરિક્ષામાં પુછાઈ શકે તેવા અનેક મુદ્દાસર પ્રશ્નો જોવા અમારી વેબસાઈટ પર રજીસ્ટર થાઓ અથવા અમારી App ફ્રી માં ડાઉનલોડ કરો.

Browse & Download CBSE Books For Class 11 All Subjects

The GSEB Books for class 10 are designed as per the syllabus followed Gujarat Secondary and Higher Secondary Education Board provides key detailed, and a through solutions to all the questions relating to the GSEB textbooks.

The purpose is to provide help to the students with their homework, preparing for the examinations and personal learning. These books are very helpful for the preparation of examination.

For more details about the GSEB books for Class 10, you can access the PDF which is as in the above given links for the same.