# NCERT Solutions for Class 11 Maths Maths Chapter 5

## Complex Numbers and Quadratic Equations Class 11

### Exercise 5.1 : Solutions of Questions on Page Number : 103

Q1 :

Express the given complex number in the form a + ib:  Q2 :

Express the given complex number in the form a + ib: i9 + i19 Q3 :

Express the given complex number in the form a + ib: i-39

Q4 :

Express the given complex number in the form a + ib: 3(7 + i7) + i(7 + i7)

Q5 :

Express the given complex number in the form a + ib: (1 - i) - (-1 + i6)

Q6 :

Express the given complex number in the form a + ib: Q7 :

Express the given complex number in the form a + ib: Q8 :

Express the given complex number in the form a + ib:  (1 - i)4

Q9 :

Express the given complex number in the form a + ib: Q10 :

Express the given complex number in the form a + ib: Q11 :

Find the multiplicative inverse of the complex number 4 - 3i

Q12 :

Find the multiplicative inverse of the complex number Q13 :

Find the multiplicative inverse of the complex number -i

Q14 :

Express the following expression in the form of a + ib. ### Exercise 5.2 : Solutions of Questions on Page Number : 108

Q1 :

Find the modulus and the argument of the complex number Q2 :

Find the modulus and the argument of the complex number Q3 :

Convert the given complex number in polar form: 1 - i

Q4 :

Convert the given complex number in polar form: - 1 + i

Q5 :

Convert the given complex number in polar form: - 1 - i

Q6 :

Convert the given complex number in polar form: -3

Q7 :

Convert the given complex number in polar form: Q8 :

Convert the given complex number in polar form: i

### Exercise 5.3 : Solutions of Questions on Page Number : 109

Q1 :

Solve the equation x2 + 3 = 0

Q2 :

Solve the equation 2x2 + x + 1 = 0

Q3 :

Solve the equation x2 + 3x + 9 = 0

Q4 :

Solve the equation -x2 + x - 2 = 0

Q5 :

Solve the equation x2 + 3x + 5 = 0

Q6 :

Solve the equation x2 - x + 2 = 0

Q7 :

Solve the equation Q8 :

Solve the equation Q9 :

Solve the equation Q10 :

Solve the equation ### Exercise Miscellaneous : Solutions of Questions on Page Number : 112

Q1 :

Evaluate: Q2 :

For any two complex numbers z1 and z2, prove that

Re (z1z2) = Re z1 Re z2 - Im z1 Im z2

Q3 :

Reduce to the standard form.

Q4 :

If x â€“ iy = prove that .

Q5 :

Convert the following in the polar form:

(i) , (ii) Q6 :

Solve the equation Q7 :

Solve the equation Q8 :

Solve the equation 27x2 - 10x + 1 = 0

Q9 :

Solve the equation 21x2 - 28x + 10 = 0

Q10 :

If find .

Q11 :

If find .

Q12 :

If a + ib = , prove that a2 + b2 = Q13 :

Let . Find

(i) , (ii) Q14 :

Find the modulus and argument of the complex number .

Q15 :

Find the real numbers x and y if (x - iy) (3 + 5i) is the conjugate of -6 - 24i.

Q16 :

Find the modulus of .

Q17 :

If (x + iy)3 = u + iv, then show that .

Q18 :

If α and ÃŽÂ² are different complex numbers with = 1, then find .

Q19 :

Find the number of non-zero integral solutions of the equation .

Q20 :

If (a + ib) (c + id) (e + if) (g + ih) = A + iB, then show that

(a2 + b2) (c2 + d2) (e2 + f2) (g2 + h2) = A2 + B2.

Q21 :

If , then find the least positive integral value of m.