Write (3 + 2i)(2 - 3i) in the form x + yi.
Answer and explanation
Correct answer: C. 12 - 5i
- Step 1: Expand: (a + bi)(c + di) = (ac - bd) + (ad + bc)i, because i^2 = -1.
- Step 2: Real part: 3 x 2 - (2)(-3) = 12. Imaginary part: 3 x -3 + (2)(2) = -5.
Answer
12 - 5i.
Why not the others: '0 - 5i' treats i^2 as +1 in the real part; '12 - 13i' uses the wrong sign in the imaginary part; '6 - 6i' multiplies real parts and imaginary parts separately.
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