What is the value of (2 + 3i) / (1 + i)? (2015)

What is the value of (2 + 3i) / (1 + i)? (2015)

Step 1: Identify the expression we need to simplify: (2 + 3i) / (1 + i).
Step 2: Find the conjugate of the denominator (1 + i). The conjugate is (1 - i).
Step 3: Multiply both the numerator and the denominator by the conjugate: (2 + 3i)(1 - i) / (1 + i)(1 - i).
Step 4: Calculate the denominator: (1 + i)(1 - i) = 1^2 - i^2 = 1 - (-1) = 1 + 1 = 2.
Step 5: Calculate the numerator: (2 + 3i)(1 - i) = 2*1 + 2*(-i) + 3i*1 + 3i*(-i) = 2 - 2i + 3i - 3 = (2 - 3) + (-2i + 3i) = -1 + i.
Step 6: Now we have: (-1 + i) / 2.
Step 7: Split the fraction: -1/2 + i/2 = -0.5 + 0.5i.

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