NCERT SOLUTIONS FOR CLASS 11 MATHS CHAPTER 5 / COMPLEX NUMBERS AND QUADRATIC EQUATIONS EX 5.1 /

Express each of the complex number given in the Exercises 1 to 10 in the form a + ib.

Question 1.

\left( 5i \right) \left( -\frac { 3 }{ 5 } i \right)

Solution.

\left( 5i \right) \left( -\frac { 3 }{ 5 } i \right)

= -3i2 = -3(-1)                    [∵ i2 = -1]

= 3 = 3 + 0i

 Question 2. i9+ i19

Solution.

NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations Ex 5.1 1

Question 3. i-39

Solution.

NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations Ex 5.1 2

Question 4. 3(7 + i7) + i(7 + i7)

Solution.

3(7 + i7) + i(7 + i7) = 21 + 21i + 7i + 7i2

= 21 + (21 + 7)i + (-1)7 = 21 – 7 + 28i

= 14 + 28i.

Ex 5.1 Class 11 Maths Question 5.

(1 – i) – (- 1 +i6)

Solution.

(1 – i) – (-1 + i6) = 1 – i + 1 – 6i

= (1 +1) – i(1 + 6)

= 2 – 7i

Question 6.

\left( \frac { 1 }{ 5 } +i\frac { 2 }{ 5 } \right) -\left( 4+i\frac { 5 }{ 2 } \right)

Solution.

NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations Ex 5.1 3

Question 7.

\left[ \left( \frac { 1 }{ 3 } +i\frac { 7 }{ 3 } \right) +\left( 4+i\frac { 1 }{ 3 } \right) \right] -\left( -\frac { 4 }{ 3 } +i \right)

Solution.

NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations Ex 5.1 4

Question 8. (1 -i)4

Solution.

(1 -i)4 = [(1 – i)2]2 = [1 – 2i + i2]2

= [1 – 2i + (-1)]2

= (-2i)2 = 4i2 = 4(-1) = – 4

= – 4 + 0i

Question 9.

{ \left( \frac { 1 }{ 3 } +3i \right) }^{ 3 }

Solution.

NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations Ex 5.1 5

Question 10.

{ \left( -2-\frac { 1 }{ 3 } i \right) }^{ 3 }

Solution.

NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations Ex 5.1 6

Find the multiplicative inverse of each of the complex numbers given in the Exercises 11 to 13.

Question 11. 4 – 3i

Solution.

NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations Ex 5.1 7

Question 12.

\sqrt { 5 } +3i

Solution.

NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations Ex 5.1 8

Question 13. -i

Solution.

NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations Ex 5.1 9

Question 14.

Express the following expression in the form of a + ib:

\frac { \left( 3+i\sqrt { 5 } \right) \left( 3-i\sqrt { 5 } \right) }{ \left( \sqrt { 3 } +\sqrt { 2 } i \right) -\left( \sqrt { 3 } -i\sqrt { 2 } \right) }

Solution.

We have, \frac { \left( 3+i\sqrt { 5 } \right) \left( 3-i\sqrt { 5 } \right) }{ \left( \sqrt { 3 } +\sqrt { 2 } i \right) -\left( \sqrt { 3 } -i\sqrt { 2 } \right) }

NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations Ex 5.1 10

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