That's really beyond the pale. It's patently obvious. If you don't assume it you can't solve the problem. But the possibility was (unknowingly) incorporated in post #3, ie, it has already been addressed.

Note: The definitions defining a complex number a+bi only apply if a and b are real.

EDIT: OK, post #3: "Gather the real and imaginary parts together in the form a+bi = 0 and equate a and b to 0."

That should have been the end of the thread. Explaining elementary arithmetic?