Question

Express the given equation in the form of a + ib, a, b ∈ R $i=\sqrt{-1}$. State the values of a and b.
$(-\sqrt{5}+2\sqrt{-4})+(1-\sqrt{-9})+(2+3i)(2-3i)$

Answer 1

As we know that

$\sqrt{ - 1} = i \\ \\ {i}^{2} = - 1$
$(-\sqrt{5}+2\sqrt{-4})+(1-\sqrt{-9})+(2+3i)(2-3i) \\ \\ ( - \sqrt{5} + 4i) + (1 -3i) + (2 + 3i)(2 - 3i) \\ \\ - \sqrt{5} + 4i + 1 - 3i + 4 + 9 \\ \\ = 14 - \sqrt{5} + i \\ \\ a + ib = 14 - \sqrt{5} + i \\ \\ a = 14 - \sqrt{5} \\ \\ b = 1$
Hope it helps you.