Question

Express the following in the form of a + ib, a, b ∈ R, i = √-1.

State the values of a and b:

(2 + 3i)(2 – 3i)

Answer 1

(2 + 3i)(2 – 3i)

= 4 – 9i²

= 4 – 9(-1) …[∵ i² = -1]

= 4 + 9

= 13

∴ (2 + 3i)(2 – 3i) = 13 + 0i

∴ a = 13 and b = 0