Question

multiply.

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

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

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

Explanation:

Expand the squared binomial

Using the Complex Numbers knowledge point

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

Simplify the terms

Using the Complex Numbers knowledge point

$$ (5-3i)^2 = 25 - 30i + 9i^2 $$

Substitute the imaginary unit power

Using the Powers of i knowledge point

$$ i^2 = -1 $$

$$ 25 - 30i + 9(-1) = 25 - 30i - 9 $$

Combine real parts

Using the Complex Numbers knowledge point

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

Answer:

Multiply.

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

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