Answer: In quadrant 1 or quadrant 2.
Step-by-step explanation:
We have the numbers:
x = c + di
y = e + fi
where c, d, e and f are real positive numbers.
the product of these numbers is:
x*y = (c + di)*(e + fi) = c*e + c*fi + d*ei ´+d*f*i^2
x*y = c*e - d*f + (c*f + d*e)i
where I used that i^2 = -1
knowing that c,f, d and e are positive numbers, then the imaginary part of the product must be always positive.
For the real part, we have c*e - d*f, that can be positive o negative depending on the values of c, e, d, and f.
So we have that the product must lie always in one of the upper two quadrants, quadrant 1 or quadrant 2 because the imaginary part is always positive and the real part can be positive or negative.
