# Thread: Determine the sq root of complex number

1. ## Determine the sq root of complex number

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

2. ## 2 answers

Originally Posted by zorro
Question : Determine the sq root of $\displaystyle (3+4i) , \ \ i=\sqrt{-1}$
this is the same as

$\displaystyle 4 + 4i - 1$
which factors to

$\displaystyle (2+i)(2+i)$

or $\displaystyle (2+i)^2$

which $\displaystyle \sqrt{(2+i)^2} = \pm(2+i )$

3. Originally Posted by zorro
Question : Determine the sq root of $\displaystyle (3+4i) , \ \ i=\sqrt{-1}$
zorro, Do you ever try to do any of the many problems that you post?
I have not seen any evidence of your work.

4. But how should i find the amplitute $\displaystyle \theta$ = $\displaystyle tan^{-1} \left( \frac{y}{x} \right)$ = $\displaystyle tan^{-1} \left( \frac{1}{2} \right)$= ?

5. ok latex error went away

Amplitude is the magnitude of change in an oscillating variable

6. No i want to know what would th amplitute be .........there is no problem with the latex

7. $\displaystyle \sqrt{\left(3+4i\right)}=\sqrt{5e^{i\theta+2\pi}}= \sqrt{5}e^{i\frac{\theta}{2}+\pi},\theta=\arctan\l eft(\frac{3}{4}\right).$

8. i know that mite i want ot know the value of $\displaystyle \theta$ , i need to find the cos and sin value with it ......

9. You have a triangle rectangle which sides are $\displaystyle 3$ and $\displaystyle 4$. Hipotenuse?

10. Originally Posted by Abu-Khalil
You have a triangle rectangle which sides are $\displaystyle 3$ and $\displaystyle 4$. Hipotenuse?
i am not getting it mite ...........the reason i am not getting is because i need the value of $\displaystyle \theta$..............and ur giving me clues which i can get it ..........

11. Originally Posted by zorro
i am not getting it mite ...........the reason i am not getting is because i need the value of $\displaystyle \theta$..............and ur giving me clues which i can get it ..........
You don't need the value of $\displaystyle \theta=\arctan\left(\frac{3}{4}\right)$, 'cause that means $\displaystyle \cos\theta=\frac{4}{5},\sin\theta=\frac{3}{5}$.

12. No u are not getting it i want to express this in polar form ........

13. 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

14. Originally Posted by bigwave

this is the same as

$\displaystyle 4 + 4i - 1$
which factors to

$\displaystyle (2+i)(2+i)$

or $\displaystyle (2+i)^2$

which $\displaystyle \sqrt{(2+i)^2} = 2+i$
Actually it's $\displaystyle 2 + i$ or $\displaystyle -(2 + i)$.

15. could anybody tell me what is the polar form of this equation ............

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