# CBSE Solutions for Class 11 English

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

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

જવાબ : 1 + 2√2i

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

જવાબ : 307/442 + 599/442 i

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

જવાબ : ¼ - ¾ i

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

જવાબ : −11/125 + 2i/125

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

જવાબ : -2+0i

Find the value of the following : i457

જવાબ : i

Find the value of the following : i528

જવાબ : 1

Find the value of the following : 1/i58

જવાબ : -1

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

જવાબ : 2i

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

જવાબ : 0

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

જવાબ : -8

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

જવાબ : 1

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

જવાબ : 2i

Evalute the following : (1+i)(1+2i)

જવાબ : −1+3i

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

જવાબ : −4/5 – 7/5 i

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

જવાબ : 3/25 – 4/25 i

Evalute the following :  (1-i)/(1+i)

જવાબ : -i

Evalute the following :  (2+i)3/2+3i

જવાબ : 37/13 + 16/13 i

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

જવાબ : −√3+i

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

જવાબ : 23/41 + 2/41 i

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

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)

જવાબ : x=3 and y=−1

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

જવાબ : x=14/15 y=15

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

જવાબ : x=5/13 and y=14/13

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

જવાબ : (63+16i)/25

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

જવાબ : 3−4i/5

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

જવાબ : 2+4i

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

જવાબ : (63+16i)/25

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

જવાબ : (3+5i)/34

Find the conjugates of  complex numbers :  4 − 5 i

જવાબ : 4+5i

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

જવાબ : √5/14 – 3/14

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

જવાબ : 4/25 + 3/25i

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

જવાબ : −1/8 − 3/√8 i

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

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

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

જવાબ : True

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

જવાબ : True

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

જવાબ : False

Solve the following  :  i6

જવાબ : -1

Solve the following  :  i5

જવાબ : i

Solve the following  :  i-2

જવાબ : -1

Solve the following  :   i-3

જવાબ : -i

Solve the following  :  i-4

જવાબ : 1

Solve the following  :   i-5

જવાબ : i

Solve the following  :   i-6

જવાબ : -1

Solve the following  :  i-7

જવાબ : -i

Solve the following  :  i2

જવાબ : -1

Solve the following  :  i2

જવાબ : -1

Solve the following  :  i3

જવાબ : -i

Solve the following  :  i4

જવાબ : 1

Find the values of i8i10 + i15

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

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

Find the values of i44 + i80 + i120

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

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.

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.

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.

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.

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).

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).

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

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

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

=0

Find the values of i40 + i80 + i120

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

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.

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.

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.

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.

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).

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).

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).

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 1 √64 A -8 2 √-64 B 8 3 -√64 C 8i

જવાબ :

1-B,2-C,3-A

 1 √49 A -7 2 √-49 B 7i 3 -√49 C 7

જવાબ :

1-C, 2-B, 3-A

 1 √25 A 6 2 √-25 B 6i 3 √-36 C 5i 4 √36 D 5

જવાબ :

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

 1 √196 A -16 2 √-196 B 16i 3 -√196 C 16

જવાબ :

1-C, 2-A, 3-B

 1 √4 A 12 2 √-4 B 12i 3 √-144 C 2i 4 √144 D 2

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

જવાબ :

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

 1 I6 A -1 2 I7 B -i 3 I8 C 1

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

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

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

જવાબ :

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