Exercise 2.2: Complex Numbers

EXERCISE 2.2

1. Evaluate the following if z = 5 - 2i and w = -1+ 3i

(i) z + w 

(ii) z - i w

(iii) 2z + 3w

(iv) zw

(v) z² + 2zw + w2

(vi) ( z + w)² .

2. Given the complex number z = 2 + 3i , represent the complex numbers in Argand diagram.

(i) z, iz , and z + iz (ii) z, - iz , and z - iz .

3. Find the values of the real numbers x and y, if the complex numbers

(3 - i)x - (2 - i) y + 2i + 5 and 2x + (-1+ 2i) y + 3 + 2i are equal.

Answers:

1. (i) 4 + i

(ii) 8 - i

(iii) 7 + 5i

(iv) 1+17i

(v) 15 + 8i 

(vi) 15 + 8i

3. x = -1 , y = 1