Finding Solutions for Complex Numbers: z^2 = 1+2i

[static]

Homework Statement

Determine all solutions of z^2 = 1+2i in the form z=a+bi, where a and b are real numbers.For this question numerical evaluation is not required. I just don't know how to start.
any clue?
thanks!

 

[Fightfish]

Reformulate 1+2i in the exponential form

 

[Hurkyl]

Determine all solutions of z^2 = 1+2i in the form z=a+bi, where a and b are real numbers.

For this question numerical evaluation is not required. I just don't know how to start.

It seems that even if you don't have a good idea how to arrive at an answer, you have an obvious starting path: plug the answer form "z=a+bi" into the equation you're trying to solve. It may, or it may not, lead to something that works, but at least it's something to try.

 

[Дьявол]

Yep, your solution is z=a+bi, just plug it in the equation, and solve the equation. You will come up with two equations (which are actually Vieta's formulas), and you can create quadratic equation and solve for a and b.

Regards.