Dividing by variable when solving algebraic equation

[Kernel Sohcahtoa]

yup, except the i is with the Sin though and Cos is the real part as you can verify if you plug in 0 into the exponential

I simply think of complex numbers as *the* way to do calculations with pairs of real numbers. The laws we use for them is basically the only way they can be if we want the usual rules of adding and multiplications to apply. I find that that makes them appear much less mysterious.

One mystery is that complex numbers seem to be intricately woven into quantum physics. Quantum amplitudes and wave functions are always complex, there doesn't seem to be a way around it...

I must say that when I learned about complex numbers from Trigonometry, 7th edition by Charles P. McKeague and Mark D. Turner, I was very fascinated with their coverage of them.  In particular, I enjoyed the following areas: trigonometric form for complex numbers; products and quotients in trigonometric form (I loved De Moivre's Theorem); roots of a complex number (this was awesome).  Hence, IMO, I found complex numbers to be quite wonderful.