Question

Create an identity using imaginary numbers, and show that the identity is true.

Answer 1

See below.

Explanation:

(3 - 2i)^2 ≡ 5 - 12i

Proof:

(3 - 2i)^2 = 3(3 - 2i) - 2i(3 - 2i)

= 9 - 6i - 6i + 4i^2

= 9 - 12i + 4(-1)

= 9 - 12i - 4

= 5 - 12i.