Question

Find the square of 6 + 8i

Answer 1

Let \(\sqrt{6+8i}\) = a + bi, where a, b ∈ R.

Squaring on both sides, we get

6 + 8i = a² + b² i² + 2abi

6 + 8i = a² – b² + 2abi ……[∵ i² = -1]

Equating real and imaginary parts, we get

a² – b² = 6 and 2ab = 8