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 z₁ = 2 – i, z₂ = -2+i Find Re

Ans. z₁ z₂ = (2 – i)(-2 + i)

11. Express in the form of a + ib (3i-7) + (7-4i) – (6+3i) + i²³

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+i² + i⁴ + i⁶ + i⁸ + ---- + i²⁰

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, w² are three cube root of unity, show that (1 – w + w²) (1 + w – w²) = 4

Ans.(1 – w + w²) (1 + w – w²)

(1 + w² - w) (1 + w – w²)

20. Find that sum product of the complex number

Ans.

21. Write the real and imaginary part 1 – 2i²

Ans. Let z = 1 – 2i²

=1 – 2 (-1)

= 1 + 2

= 3

= 3 + 0.i

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

22. If two complex number z₁, z₂ are such that |z₁| = |z₂|, is it then necessary that z₁ = z₂

Ans.Let z₁ = 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 x² + y² = 1

Ans.

taking conjugate both side

x² + y² = 1

[i² = -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 a²+b² = 1 and

Ans.

a² + b² = 1

7.If z₁ = 2-i and Z₂ = 1+i Find

Ans.z₁ + z₂ + 1 = 2 – i + 1+ i + 1 = 4

8.If (p + iq)² = x + iy Prove that (p² + q²)² = x² + y²

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.i²⁵ + (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) y² + (6+i) and (2+i) x

Ans.(1+i) y² + (6 + i) = (2 + i) x

y² + iy² + 6 + i = 2x + xi

(y² + 6) + (y² + 1) i = 2x + xi

y² + 6 = 2x

y² + 1 = x

y ² = x – 1

x – 1 + 6 = 2x

5 = x

17.If x + iy =

Ans.

taking conjugate both side

x² + y² = 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 – 5yi² = - 6 + 24i

20.If

Ans.If