Let z = 3 + 4i and w = 1 - 2i. What is the imaginary part of z / w?
Show the answer and explanation
Correct answer
A. 2
Principle or equation
To divide complex numbers, multiply numerator and denominator by the conjugate of the denominator, then simplify.
Why this answer is correct
z/w = (3+4i)/(1-2i). Multiply by conjugate (1+2i): (3+4i)(1+2i)/(1+4) = (3+6i+4i+8i^2)/5 = (3+10i-8)/5 = (-5+10i)/5 = -1+2i. Imaginary part is 2.
Example
For z=1+i, w=1-i, z/w = (1+i)^2/(1+1)= (1+2i-1)/2 = i, imaginary part 1.
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