Exercise 2.4: Conjugate of a Complex Number

EXERCISE 2.4

1. Write the following in the rectangular form:

2. If z = x + iy , find the following in rectangular form.

3. If z = 2 - i and z2 = -4 + 3i , find the inverse of z1z2 and z1 /z1

4. The complex numbers u, v , and w are related by 

If v = 3 - 4i and w = 4 + 3i , find u in rectangular form.

5. Prove the following properties:

(i) z is real if and only if z = 

(ii) 

6. Find the least value of the positive integer n for which (√3+i)n

(i) real (ii) purely imaginary

7. Show that (i) (2+i√3)10 - (2-i√3)10 is  purely imaginary

  is real.

Answers: