Let z = 1 - 2i and w = 3 + i. What is the imaginary part of z / w?
Show the answer and explanation
Correct answer
A. -7/10
Principle or equation
To divide complex numbers, multiply numerator and denominator by the conjugate of the denominator.
Why this answer is correct
z/w = (1 - 2i)/(3 + i) * (3 - i)/(3 - i) = ((1 - 2i)(3 - i))/(9 + 1) = (3 - i - 6i + 2i^2)/10 = (3 - 7i - 2)/10 = (1 - 7i)/10 = 1/10 - (7/10)i. The imaginary part is -7/10.
Example
For (2 + i)/(1 - i), multiply by (1 + i)/(1 + i) to get (1 + 3i)/2, imaginary part 3/2.
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