What are two complex numbers whose product is 10?

Answer 1

The set of complex numbers includes the set of real numbers. The real number system is just with the imaginary part set to 0.

example: z = 5 + i0 = 5

So the simple answer would be (2+i0)*(5+i0) = 10, so the complex values (2,0) and (5,0) get the result your looking for.

If you want a pair not on the real line then 2*exp(i*pi/4) and 5*exp(-i*pi/4) will do.

If you multiply the two complex numbers you get 2*5*exp(i*(pi/4-pi/4)) which is just 10.

Since pure imaginary numbers are also part of the set of complex numbers, you could have -2i * 5i, the i's multiplied together yield -1 and multiplied by -10 = 10.