Question

practice assignment 2.4 complex numbers
score: 130/250 answered: 13/25
question 14
evaluate the expression (4 - 2i)(-4 + 4i) and write the result in the form a + bi.
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Explanation:

Step1: Use the FOIL method

$$(4 - 2i)(-4 + 4i)=4\times(-4)+4\times4i-2i\times(-4)-2i\times4i$$

Step2: Calculate each term

• \(4\times(-4)=-16\)
• \(4\times4i = 16i\)
• \(-2i\times(-4)=8i\)
• \(-2i\times4i=-8i^{2}\)

Since \(i^{2}=-1\), then \(-8i^{2}=-8\times(-1) = 8\)

Step3: Combine like - terms

\(-16 + 16i+8i + 8=(-16 + 8)+(16i+8i)\)
\(=-8 + 24i\)

Answer:

\(-8 + 24i\)