Question

Simplify the given and express in the form of a + ib.
(2 + 3i)(1 - 4i)

Answer 1

To simplify the expression , multiply the expression first

$(2 + 3i)(1 - 4i) \\ \\ = 2 - 8i + 3i - 12 {i}^{2} \\ \\ because \: {i}^{2} = - 1 \\ \\ so \\ \\ = 2 - 5i - 12( - 1) \\ \\ = 2 - 5i + 12 \\ \\ = 14 - 5i \\ \\ so \\ \\ a + ib = 14 - 5i \\ \\ a = 14 \\ \\ b = - 5$
Hope it helps you.