Author Topic: how to find the square root of a complex number? (Read 3497 times) Tweet Share

1i1ii1i · « **on:** April 09, 2012, 01:27:46 pm »

how do you work out the square roots of -15-8i and 24+7i ?

ggxoxo · « **Reply #1 on:** April 09, 2012, 01:36:16 pm »

Dont you have to let z^2=-15-8i and z^2=24+7i and the solve for z.

You can use De Moivre's theorem, etc

1i1ii1i · « **Reply #2 on:** April 09, 2012, 01:43:55 pm »

how can you?

Somye · « **Reply #3 on:** April 10, 2012, 10:19:28 pm »

If you're looking at a Cartesian method, first let $z^2 = -15-8i$ and $z= a+bi$
Then, $-15-8i = a^2 - b^2+2abi$
Equating coefficients, you get $-15 = a^2 - b^2$ and $ab = -4$
Sub in $b = -4/a$ to get $a^4 + 15a^2 - 16 = 0$
$(a^2+ 16)(a^2 - 1)$ but $a^2$ is a part of R so
$a^1 = 1, a = 1, -1$
therefore $b= -4, 4$
and your roots are $1-4i$ and $-1+4i$

apply a similar technique to the second one

mr.politiks · « **Reply #4 on:** April 10, 2012, 10:29:00 pm »

When you get to the stage where you can start converting things to polar in your head then go straight to polar form for anything that isnt addition or subtraction and as long as it is easy to do so. In this case it wasn't tho!

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Author Topic: how to find the square root of a complex number? (Read 3497 times) Tweet Share

1i1ii1i

how to find the square root of a complex number?

ggxoxo

Re: how to find the square root of a complex number?

1i1ii1i

Re: how to find the square root of a complex number?

Somye

Re: how to find the square root of a complex number?

mr.politiks

Re: how to find the square root of a complex number?

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