Complex numbers (5+2i)=SQRT(x+iy)

[johnwalton84]

How do you evaluate this type of problem:

(5+2i)=SQRT(x+iy)

 

[Muzza]

Have you considered raising both sides to the power of 2? Or writing both sides in polar form?

 

[johnwalton84]

Yes, but when you do that the i value on the left disappears and you get

21 = x+iy

which suggests that there is no imaginary part of the solution (?)


I haven't tried writing both sides in polar form, i'll try that now

 

[Muzza]

Yes, but when you do that the i value on the left disappears and you get

21 = x+iy

No, since (5 + 2i)^2 is NOT equal to 5^2 + (2i)^2.

(5 + 2i)^2 = (5 + 2i)(5 + 2i) = 5*5 + 5*2i + 2i*5 + 2i*2i = 25 + 10i + 10i - 4, etc.

 

[johnwalton84]

of course

thanks

it works fine in polars as well