What is the value of (3 + 2i) / (1 - i)?
Show the answer and explanation
Correct answer
A. 1/2 + 5/2 i
Principle or equation
To divide complex numbers, multiply numerator and denominator by the conjugate of the denominator.
Why this answer is correct
Multiply numerator and denominator by (1 + i): (3 + 2i)(1 + i) / ((1 - i)(1 + i)) = (3 + 3i + 2i + 2i^2) / (1 - i^2) = (3 + 5i - 2) / (1 + 1) = (1 + 5i) / 2 = 1/2 + (5/2)i.
Example
For (2 + i)/(1 + i), multiply by (1 - i) to get (2 - 2i + i - i^2)/2 = (3 - i)/2 = 3/2 - 1/2 i.
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