Question

Find the square root of complex number −8−6i

Comments

Thank you so much

Answer 1

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

Squaring on both sides, we get

– 8 – 6i = (a + bi)²

∴ – 8 – 6i = a² + b²i² + 2abi

∴ – 8 – 6i = (a² – b²) + 2abi ..... [∵ i² = – 1]

Equating real and imaginary parts, we get

a² – b² = – 8 and 2ab = – 6

∴ a² – b² = – 8 and b = \(\frac{-3}{a}\)