Question

multiply.
(2 - 2i)(1 - 4i)
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:
$(2 - 2i)(1 - 4i) = 2 \cdot 1 + 2 \cdot (-4i) - 2i \cdot 1 + (-2i) \cdot (-4i)$

Step2: Simplify each product

Calculate each term:
$2 \cdot 1 = 2$
$2 \cdot (-4i) = -8i$
$-2i \cdot 1 = -2i$
$(-2i) \cdot (-4i) = 8i^2$

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

Replace \(i^2\) with \(-1\):
$8i^2 = 8(-1) = -8$

Step4: Combine like terms

Combine the real parts and the imaginary parts:
Real: \(2 - 8 = -6\)
Imaginary: \(-8i - 2i = -10i\)

Answer:

\(-6 - 10i\)