Write (2 - 3i)(4 + i) in the form x + yi.
Answer and explanation
Correct answer: C. 11 - 10i
- Step 1: Expand: (a + bi)(c + di) = (ac - bd) + (ad + bc)i, because i^2 = -1.
- Step 2: Real part: 2 x 4 - (-3)(1) = 11. Imaginary part: 2 x 1 + (-3)(4) = -10.
Answer
11 - 10i.
Why not the others: '5 - 10i' treats i^2 as +1 in the real part; '11 + 14i' uses the wrong sign in the imaginary part; '8 - 3i' multiplies real parts and imaginary parts separately.
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