Write (1 - i)(2 + 2i) in the form x + yi.
Answer and explanation
Correct answer: A. 4 + 0i
- Step 1: Expand: (a + bi)(c + di) = (ac - bd) + (ad + bc)i, because i^2 = -1.
- Step 2: Real part: 1 x 2 - (-1)(2) = 4. Imaginary part: 1 x 2 + (-1)(2) = 0.
Answer
4 + 0i.
Why not the others: '0 + 0i' treats i^2 as +1 in the real part; '4 + 4i' uses the wrong sign in the imaginary part; '2 - 2i' multiplies real parts and imaginary parts separately.
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