How do you figure out complex number problems?

Answer 1

It depends on what you're trying to do with the complex numbers, and what level of math understanding that you are at. Some tips:

Treat the i like a variable (like x): example: Add a + bx & c + dx = a + bx + c + dx = a + c + bx + dx = (a + c) + (b + d)x. Now, substitute x = i

Multiplying: (a + bx) * (c + dx) = ac + adx + bcx + bdx2 = ac + (ad + bc)x + bdx2, when substituting x = i in this one: ac + (ad + bc)i + bdi2, but i2 = -1, so we have:

ac + (ad + bc)i - bd = (ac - bd) + (ad + bc)i

If you are familiar with vectors, you can treat complex numbers as vectors in the complex plane, and do some operations on them that way. See related link.