What Methods Solve (x+iy)^2 = 5+4i?

[alijan kk]

Homework Statement

What is the value of x and y , when (x+iy) ^2=5+4i?

Homework Equations

The Attempt at a Solution

(x+iy)^2=5+4i

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

 

[berkeman]

Homework Statement

What is the value of x and y , when (x+iy) ^2=5+4i?

Homework Equations

The Attempt at a Solution

(x+iy)^2=5+4i

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

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

 

[Buffu]

Homework Statement

What is the value of x and y , when (x+iy) ^2=5+4i?

Homework Equations

The Attempt at a Solution

(x+iy)^2=5+4i

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

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.

 

[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.

 

[Ray Vickson]

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.

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.

 

[mpresic]

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