Write (1 + 5i)(1 + i) in the form x + yi.

Answer and explanation

Correct answer: C. -4 + 6i

  1. Step 1: Expand: (a + bi)(c + di) = (ac - bd) + (ad + bc)i, because i^2 = -1.
  2. Step 2: Real part: 1 x 1 - (5)(1) = -4. Imaginary part: 1 x 1 + (5)(1) = 6.
Answer
-4 + 6i.
Why not the others: '6 + 6i' treats i^2 as +1 in the real part; '-4 - 4i' uses the wrong sign in the imaginary part; '1 + 5i' multiplies real parts and imaginary parts separately.

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