# How do i solve this kind of equations?

1. May 17, 2017

### alijan kk

1. The problem statement, all variables and given/known data
What is the value of x and y , when (x+iy) ^2=5+4i?

2. Relevant equations

3. The attempt at a solution
(x+iy)^2=5+4i

x^2+2xiy-y^2=5+4i

Last edited by a moderator: May 17, 2017
2. May 17, 2017

### Staff: Mentor

Good. Now keep going -- equate the real and imaginary parts and solve the 2 simultaneous equations...

3. May 17, 2017

### Buffu

Equate the imagnary and real part. Like if $x +iy = 3+i5$ then I equate to get $x = 3$ and $y = 5$.
Though there are other ways to take square root of complex numbers.

EDIT :
I did not see post by @berkeman. Sorry don't mean to copy it.

4. May 17, 2017

### mpresic

The two equations are difficult to solve simultaneously. You can solve graphically for the intercept. Both equations are hyperbolas (one is rotated). Alternatively to solve without graphics you should express 5 + 4i in polar form and then take the square root.

5. May 17, 2017

### Ray Vickson

They are not very difficult to solve simultaneously. Using the equation for the imaginary part gives a formula for y in terms of x. Then substituting that formula into the equation for the real part gives a quadratic equation in x2, which is easily solved using standard formulas.

6. May 17, 2017

### mpresic

Yes, That is interesting. Expressing in polar form and taking square root is OK too.