# Square root of complex number [duplicate]

How do I find the square root of complex number $7-(6\sqrt2)i$?

I hope there's someone who can show me the method. Thanks in advance.

## marked as duplicate by David K, Hans Lundmark, iadvd, Shailesh, Eric StuckyOct 5 '16 at 2:12

• There is no "THE squareroot of a complex number". It is better to write "Solve the equation $x^2=7-(6\sqrt{2})i$ for $x$ and you get two answers, neither of them being positive or negative since they also will be...complex – imranfat Oct 4 '16 at 17:40
• We'll need to write this in the form $re^{i\theta}$ and use de Moivre. – Sean Roberson Oct 4 '16 at 17:40
• try $a + b i \sqrt 2,$ squre it and see if you get $a,b$ integers or at least rational. $3 - i \sqrt 2$ works, did it in my head – Will Jagy Oct 4 '16 at 17:42
$$\sqrt{7-6\sqrt{2}i}=\sqrt{7+2-2-6\sqrt{2}i}=\sqrt{9-6\sqrt{2}i-2}=\sqrt{3^2-2*3\sqrt{2}i+(\sqrt2i)^2}=\sqrt{(3-\sqrt{2}i)^2}$$