Write (4 + i)(3 - i) in the form x + yi.
Answer and explanation
Correct answer: B. 13 - i
- Step 1: Expand: (a + bi)(c + di) = (ac - bd) + (ad + bc)i, because i^2 = -1.
- Step 2: Real part: 4 x 3 - (1)(-1) = 13. Imaginary part: 4 x -1 + (1)(3) = -1.
Answer
13 - i.
Why not the others: '11 - i' treats i^2 as +1 in the real part; '13 - 7i' uses the wrong sign in the imaginary part; '12 - i' multiplies real parts and imaginary parts separately.
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