Write (2 + i)(1 + 3i) in the form x + yi.
Answer and explanation
Correct answer: C. -1 + 7i
- Step 1: Expand: (a + bi)(c + di) = (ac - bd) + (ad + bc)i, because i^2 = -1.
- Step 2: Real part: 2 x 1 - (1)(3) = -1. Imaginary part: 2 x 3 + (1)(1) = 7.
Answer
-1 + 7i.
Why not the others: '5 + 7i' treats i^2 as +1 in the real part; '-1 + 5i' uses the wrong sign in the imaginary part; '2 + 3i' multiplies real parts and imaginary parts separately.
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