# Thread: solving comple number

1. ## solving comple number

how to solve
sqrt (1 + j1049.3)(j0.075)

i try it but.. keep on getting negative answer..
the answer should be 0.004 + j8.87

2. ## Re: solving comple number

Originally Posted by nameck
how to solve
sqrt (1 + j1049.3)(j0.075)

i try it but.. keep on getting negative answer..
the answer should be 0.004 + j8.87
Is this $\displaystyle \displaystyle \sqrt{1 + 1049.3i}\left(0.075i\right)$ or $\displaystyle \displaystyle \sqrt{\left(1 + 1049.3i\right)\left(0.075i\right)}$?

3. ## Re: solving comple number

Originally Posted by Prove It
Is this $\displaystyle \displaystyle \sqrt{1 + 1049.3i}\left(0.075i\right)$ or $\displaystyle \displaystyle \sqrt{\left(1 + 1049.3i\right)\left(0.075i\right)}$?
$\displaystyle \displaystyle \sqrt{\left(1 + 1049.3i\right)\left(0.075i\right)}$
is there any trick to solve this kind of equation?

4. ## Re: solving comple number

Originally Posted by nameck
$\displaystyle \displaystyle \sqrt{\left(1 + 1049.3i\right)\left(0.075i\right)}$
is there any trick to solve this kind of equation?
Start by expanding, then convert to polars and use DeMoivre's Theorem.

5. ## Re: solving comple number

Originally Posted by nameck
how to solve
sqrt (1 + j1049.3)(j0.075)
i try it but.. keep on getting negative answer..
the answer should be 0.004 + j8.87
As you can see here the given answer is correct.

What are you using to calculate the value?
What is the source and text of the original question?

6. ## Re: solving comple number

Originally Posted by Plato
As you can see here the given answer is correct.

What are you using to calculate the value?
What is the source and text of the original question?
ya.. i get the answer from wolfram also..

i'm using DeMoivre's theorem.. still cannot get the correct answer..
question is about transmission line..
i need solve the complex number to get the value of propagation constant..

and still i didn't get the correct answer.. got any idea to solve it Plato?

7. ## Re: solving comple number

Originally Posted by nameck
and still i didn't get the correct answer.. got any idea to solve it Plato?
Well $\displaystyle (1+1049i)(0.075)i=-78.69+0.075i$.
Because real part is negative the argument is $\displaystyle \theta=\pi+\arctan\left(\frac{-0.075}{78.69}\right)$
and $\displaystyle |-78.69+0.075i|=78.697$.
Go from there.

8. ## Re: solving comple number

should i apply DeMoivre's Theorem?

9. ## Re: solving comple number

Originally Posted by nameck
should i apply DeMoivre's Theorem?
$\displaystyle \sqrt{78.697}\cdot\exp\left(\frac{\theta i}{2}\right)$
gives the correct answer.

10. ## Re: solving comple number

got it!
change to polar form first.. then change to rectangular form back..
then.. Walla! got the answer.. thanks guys.. =)