What is the value of (3 + 4i) / (1 + i)? (2021)

What is the value of (3 + 4i) / (1 + i)? (2021)

Step 1: Identify the expression to simplify: (3 + 4i) / (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: (3 + 4i)(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: (3 + 4i)(1 - i) = 3*1 + 3*(-i) + 4i*1 + 4i*(-i) = 3 - 3i + 4i - 4 = (3 - 4) + (-3i + 4i) = -1 + i.
Step 6: Combine the results: The expression now is (-1 + i) / 2.
Step 7: Split the fraction: -1/2 + i/2 = -0.5 + 0.5i.
Step 8: Convert to standard form: This can also be written as 2 + i.

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