Question

4. Find the value of the real number y such that

(3+2i)(1 + iy)
is :
(a) real
(b) imaginary

Answer 1

Explanation:

(3 + 2i)(1 + iy)

= 3 + (3y + 2)i - 2y (because i² = -1)

For this to be real, (3y + 2) = 0. => y = -2/3

For this to be imaginary, y can be any real or complex number (except -2/3)