Answers: First Quadrant and Fourth Quadrant
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Explanation:
Let
be the two complex numbers.
Multiply them out to see what we get
![w*z = (c+di)(e-fi)\\\\w*z = c(e-fi)+di(e-fi)\\\\w*z = ce-cf*i+de*i-df*i^2\\\\w*z = ce-cf*i+de*i-df*(-1)\\\\w*z = ce-cf*i+de*i+df\\\\w*z = (ce+df)+(-cf+de)*i\\\\](https://tex.z-dn.net/?f=w%2Az%20%3D%20%28c%2Bdi%29%28e-fi%29%5C%5C%5C%5Cw%2Az%20%3D%20c%28e-fi%29%2Bdi%28e-fi%29%5C%5C%5C%5Cw%2Az%20%3D%20ce-cf%2Ai%2Bde%2Ai-df%2Ai%5E2%5C%5C%5C%5Cw%2Az%20%3D%20ce-cf%2Ai%2Bde%2Ai-df%2A%28-1%29%5C%5C%5C%5Cw%2Az%20%3D%20ce-cf%2Ai%2Bde%2Ai%2Bdf%5C%5C%5C%5Cw%2Az%20%3D%20%28ce%2Bdf%29%2B%28-cf%2Bde%29%2Ai%5C%5C%5C%5C)
The result we get is in the form a+bi where
- a = ce+df = real part
- b = -cf+de = imaginary part
Recall that any complex number of the form a+bi can be plotted on the xy plane with 'a' being treated as the x coordinate and b as the y coordinate. In short, the location of a+bi is at the point (a,b)
With c,d,e,f being positive, this means ce and df are positive, and a = ce+df is also positive.
This places the result of wz in either the first or fourth quadrants (the northeast or southeast quadrants respectively), due to the positive x coordinate.
We don't have enough info to determine whether b = -cf+de is positive or not. So that's why we can't nail down the precise quadrant of wz
If b > 0, then wz is in quadrant 1
If b < 0, then wz is in quadrant 4