Question : Determine the sq root of $\displaystyle (3+4i) , \ \ i=\sqrt{-1}$

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- Dec 28th 2009, 11:48 AMzorroDetermine the sq root of complex number
Question : Determine the sq root of $\displaystyle (3+4i) , \ \ i=\sqrt{-1}$

- Dec 28th 2009, 12:00 PMbigwave2 answers
- Dec 28th 2009, 12:01 PMPlato
- Dec 28th 2009, 12:25 PMzorro
But how should i find the amplitute $\displaystyle \theta$ = $\displaystyle tan^{-1} \left( \frac{y}{x} \right)$ = $\displaystyle tan^{-1} \left( \frac{1}{2} \right)$= ?

- Dec 28th 2009, 12:42 PMbigwave
ok latex error went away

Amplitude is the magnitude of change in an oscillating variable - Dec 28th 2009, 12:43 PMzorro
No i want to know what would th amplitute be .........there is no problem with the latex

- Dec 28th 2009, 01:52 PMAbu-Khalil
$\displaystyle \sqrt{\left(3+4i\right)}=\sqrt{5e^{i\theta+2\pi}}= \sqrt{5}e^{i\frac{\theta}{2}+\pi},\theta=\arctan\l eft(\frac{3}{4}\right).$

- Dec 28th 2009, 02:07 PMzorro
i know that mite i want ot know the value of $\displaystyle \theta$ , i need to find the cos and sin value with it ......

- Dec 28th 2009, 02:16 PMAbu-Khalil
You have a triangle rectangle which sides are $\displaystyle 3$ and $\displaystyle 4$. Hipotenuse?

- Dec 28th 2009, 02:32 PMzorro
- Dec 28th 2009, 02:47 PMAbu-Khalil
- Dec 28th 2009, 03:25 PMzorro
No u are not getting it i want to express this in polar form ........

- Dec 28th 2009, 03:46 PMAlso sprach Zarathustra
3+4i=5(cos(38.86...+2pi*k)* + isin(36.86...+2pi*k)*)=5cis(36.86... +2pi*k)*

square root of above can be calculate with de Moivre formula.

De Moivre's formula - Wikipedia, the free encyclopedia - Dec 28th 2009, 03:55 PMProve It
- Dec 28th 2009, 05:14 PMzorro
could anybody tell me what is the polar form of this equation ............