Question

multiply.
(6 - 4i)(-5 + i)
write your answer as a complex number in standard form.

Explanation:

Step1: Apply distributive property (FOIL)

Multiply each term in the first complex number by each term in the second:
$(6 - 4i)(-5 + i) = 6(-5) + 6(i) - 4i(-5) - 4i(i)$

Step2: Simplify each product

Calculate each term:
$6(-5) = -30$,
$6(i) = 6i$,
$-4i(-5) = 20i$,
$-4i(i) = -4i^2$.

Step3: Substitute \(i^2 = -1\)

Replace \(i^2\) with \(-1\) in the last term:
$-4i^2 = -4(-1) = 4$.

Step4: Combine like terms

Combine the real parts and the imaginary parts:
Real parts: \(-30 + 4 = -26\),
Imaginary parts: \(6i + 20i = 26i\).

Answer:

\(-26 + 26i\)