Let z = 2 - i and w = 3 + 2i. What is the real part of z * w?
Show the answer and explanation
Correct answer
A. 8
Principle or equation
To multiply complex numbers, use the distributive law and i^2 = -1. The real part is the sum of the products of the real parts and the negative of the product of the imaginary parts.
Why this answer is correct
z * w = (2 - i)(3 + 2i) = 6 + 4i - 3i - 2i^2 = 6 + i + 2 = 8 + i. The real part is 8.
Example
For (1 + 2i)(3 - i) = 3 - i + 6i - 2i^2 = 3 + 5i + 2 = 5 + 5i, real part 5.
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