I understand the process of switching back to Complex form. However, there's one part that I don't understand where the answer comes from. Example:
Express 2(cos 2pi/3 + i sin 2pi/3) in rectangular form. The polar coordinate is (2, 2pi/3). That I understand.
Now, when you start to simplify the problem, it comes out to be;
2(-1/2 + i sqrt3/2) "sqrt" meaning square root of, as in the square root of 3.
I get where the negative one half came from. But the square root of three over two is where I'm lost. When I put into my calculator, "sin(2pi/3)" I get a really long decimal. Eventually, the answer comes out to be;
-1 + isqrt3.
I understand how they got -1. But if someone could PLEASE explain the square root of three over two I'd really appreciate it. Thank you!