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

AI Thread Summary
To evaluate the equation (5+2i)=SQRT(x+iy), raising both sides to the power of 2 is suggested, leading to 21 = x + iy, which indicates no imaginary part in the solution. However, it is clarified that (5 + 2i)^2 does not equal 5^2 + (2i)^2, as the correct expansion includes both real and imaginary components. The discussion also touches on the potential of using polar form for further evaluation, with participants confirming that this method works effectively. Overall, the conversation emphasizes the importance of correctly handling complex number operations. The insights shared can aid in understanding complex number equations better.
johnwalton84
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How do you evaluate this type of problem:

(5+2i)=SQRT(x+iy)
 
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Have you considered raising both sides to the power of 2? Or writing both sides in polar form?
 
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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
 
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.
 
:blushing: of course :blushing:

:smile: thanks

it works fine in polars as well
 

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