What are the values of x and y for the complex number z=\sqrt{3+4i}?

[Stroodle]

$$z=x+yi$$ determine the values of x and y such that $$z=\sqrt{3+4i}$$
I'm not even sure where to start with this one, so any help would be greatly appreciated

 

[n!kofeyn]

So basically the question you are given is find x and y where
$$x+yi=\sqrt{3+4i}$$.
Start off by squaring both sides, then go about solving for x and y. When solving variables with complex numbers, you usually equate the real and imaginary parts of both sides. In other words, if you have x+iy=u+iv, then x=u and y=v. This should get you going. Let us know if you are still stuck.

 

[HallsofIvy]

In other words, find the square root of 3+4i. Of course, there are two square roots - the problem said "values"- so n!kofeyn's equations will have two solutions. You could also do this problem by converting to "polar" form and applying deMoivre's formula. That was my first thought but n!kofeyn's idea is simpler and more straightforward.

 

[Stroodle]

Awesome. I've got it now. Thanks for your help.

 

[n!kofeyn]

No problem.