Question

multiply.

\\((5-3i)^2\\)

\\((5-3i)^2 = \square\\)

(simplify your answer. type your answer in the form \\(a + bi\\).)

Explanation:

Expand the squared expression

Using the Complex Numbers knowledge point

$$ (5 - 3i)^2 = (5 - 3i)(5 - 3i) = 5^2 - 2(5)(3i) + (3i)^2 $$

Simplify the terms

Using the Complex Numbers knowledge point

$$ 25 - 30i + 9i^2 $$

Substitute the imaginary unit power

Using the Powers of i knowledge point

$$ i^2 = -1 \implies 25 - 30i + 9(-1) $$

Combine the real parts

Using the Complex Numbers knowledge point

$$ 25 - 9 - 30i = 16 - 30i $$

Answer:

Multiply.

$$(5-3i)^2$$

\((5-3i)^2 =\) <blank>\(16-30i\)</blank>
(Simplify your answer. Type your answer in the form \(a + bi\).)