# Important Questions for CBSE Class 11 Maths Chapter 5 - Complex Numbers and Quadratic Equations

## CBSE Class 11 Maths Chapter-5 Important Questions - Free PDF Download

**1 Marks Questions**

**1. Evaluate i ^{-39}**

**Ans. **

**2. Solved the quadratic equation **

**Ans. **

**3. If = 1, then find the least positive integral value of m. **

**Ans. **

**4. Evaluate (1+ i) ^{4} **

**Ans. **

**5. Find the modulus of **

**Ans. **Let z =

**6. Express in the form of a + ib. (1+3i) ^{-1}**

**Ans. **

**7. Explain the fallacy in -1 = i. i. = **

**Ans. ** is okay but

is wrong.

**8. Find the conjugate of **

**Ans. **Let z =

**9. Find the conjugate of – 3i – 5.**

**Ans. **Let z = 3i – 5

**10. Let z _{1} = 2 – i, z_{2} = -2+i Find Re **

**Ans. **z_{1} z_{2} = (2 – i)(-2 + i)

**11. Express in the form of a + ib (3i-7) + (7-4i) – (6+3i) + i ^{23}**

**Ans. **Let

Z =

**12. Find the conjugate of **

**Ans. **

**13. Solve for x and y, 3x + (2x-y) i= 6 – 3i**

**Ans. **3x = 6

x = 2

2x – y = - 3

2 × 2 – y = - 3

- y = - 3 – 4

y = 7

**14. Find the value of 1+i ^{2} + i^{4} + i^{6} + i^{8} + ---- + i^{20}**

**Ans.**

**15. Multiply 3-2i by its conjugate.**

Ans.Let z = 3 – 2i

**16. Find the multiplicative inverse 4 – 3i.**

**Ans. **Let z = 4 – 3i

**17. Express in term of a + ib **

**Ans. **

**18. Evaluate **

**Ans.**

**19. If 1, w, w ^{2} are three cube root of unity, show that (1 – w + w^{2}) (1 + w – w^{2}) = 4**

**Ans**.(1 – w + w^{2}) (1 + w – w^{2})

(1 + w^{2} - w) (1 + w – w^{2})

**20. Find that sum product of the complex number **

**Ans. **

**21. Write the real and imaginary part 1 – 2i ^{2}**

**Ans. **Let z = 1 – 2i^{2}

=1 – 2 (-1)

= 1 + 2

= 3

= 3 + 0.i

Re (z) = 3, Im (z) = 0

**22. If two complex number z _{1}, z_{2 }are such that |z_{1}| = |z_{2}|, is it then necessary that z_{1} = z_{2 }**

**Ans.**Let z_{1} = a + ib

**23. Find the conjugate and modulus of **

**Ans. **Let

**24. Find the number of non zero integral solution of the equation |1-i| ^{x} = 2^{x}**

**Ans. **

Which is false no value of x satisfies.

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

**Ans. **

**4 Marks Questions**

**1.If x + ί y = Prove that x ^{2} + y^{2} = 1**

**Ans.**

taking conjugate both side

x^{2} + y^{2} = 1

[i^{2} = -1

**2.Find real ****θ**** such that is purely real. **

**Ans.**

For purely real

Im (z) = 0

**3.Find the modulus of **

**Ans.**

**4.If then Show that **

**Ans.**

**5.If x – iy = Prove that **

**Ans.**

Taking conjugate both side

**6.If , where a, b, c are real prove that a ^{2}+b^{2} = 1 and **

**Ans.**

a^{2} + b^{2} = 1

**7.If z _{1} = 2-i and Z_{2} = 1+i Find **

**Ans.**z_{1} + z_{2} + 1 = 2 – i + 1+ i + 1 = 4

**8.If (p + iq) ^{2 }= x + iy Prove that (p^{2} + q^{2})^{2} = x^{2} + y^{2}**

**Ans.(**p + iq)^{2} = x + iy (i)

Taking conjugate both side

(p – iq)^{2} = x –iy (ii)

(i) × (ii)

**9.If **

**Ans.**

Taking conjugate both side

**10.If **

**Ans.**

**11.Solve **

**Ans.**

**12.Find the modulus **

**Ans**.i^{25} + (1+3i)^{3}

**13.If **

**Ans.** (i) (Given)

(ii) [taking conjugate both side

(i) × (ii)

**14.Evaluate **

**Ans. **

**15.Find that modulus and argument **

**Ans.**

**16.For what real value of x and y are numbers equal (1+i) y ^{2} + (6+i) and (2+i) x**

**Ans.**(1+i) y^{2} + (6 + i) = (2 + i) x

y^{2} + iy^{2} + 6 + i = 2x + xi

(y^{2} + 6) + (y^{2} + 1) i = 2x + xi

y^{2} + 6 = 2x

y^{2} + 1 = x

y ^{2} = x – 1

x – 1 + 6 = 2x

5 = x

**17.If x + iy = **

**Ans.**

taking conjugate both side

x^{2} + y^{2} = 1

Proved.

**18.Convert in the polar form **

**Ans.**

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

**Ans.**

(x – iy) (3 + 5i) = - 6 + 24i

3x + 5xi – 3yi – 5yi^{2} = - 6 + 24i

**20.If **

**Ans.**If

**6 Marks Questions**

**1.If z = x + i y and w = Show that |w| = 1 **

**Ans.** w =

**2.Convert into polar form **

**Ans.**

Since Re (z) < o, and Im (z) > o

**3.Find two numbers such that their sum is 6 and the product is 14.**

**Ans.**Let x and y be the no.

x + y = 6

xy = 14

**4.Convert into polar form **

**Ans.**

**5.If ****α**** and ****β**** are different complex number with |****β****| = 1 Then find **

**Ans.**