# solving comple number

• Sep 13th 2011, 06:57 AM
nameck
solving comple number
how to solve
sqrt (1 + j1049.3)(j0.075)

the answer should be 0.004 + j8.87
• Sep 13th 2011, 07:00 AM
Prove It
Re: solving comple number
Quote:

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

the answer should be 0.004 + j8.87

Is this $\displaystyle \sqrt{1 + 1049.3i}\left(0.075i\right)$ or $\displaystyle \sqrt{\left(1 + 1049.3i\right)\left(0.075i\right)}$?
• Sep 13th 2011, 07:02 AM
nameck
Re: solving comple number
Quote:

Originally Posted by Prove It
Is this $\displaystyle \sqrt{1 + 1049.3i}\left(0.075i\right)$ or $\displaystyle \sqrt{\left(1 + 1049.3i\right)\left(0.075i\right)}$?

$\displaystyle \sqrt{\left(1 + 1049.3i\right)\left(0.075i\right)}$
is there any trick to solve this kind of equation?
• Sep 13th 2011, 07:04 AM
Prove It
Re: solving comple number
Quote:

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

Start by expanding, then convert to polars and use DeMoivre's Theorem.
• Sep 13th 2011, 08:53 AM
Plato
Re: solving comple number
Quote:

Originally Posted by nameck
how to solve
sqrt (1 + j1049.3)(j0.075)
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?
• Sep 13th 2011, 09:02 AM
nameck
Re: solving comple number
Quote:

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..
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?
• Sep 13th 2011, 09:25 AM
Plato
Re: solving comple number
Quote:

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

Well $(1+1049i)(0.075)i=-78.69+0.075i$.
Because real part is negative the argument is $\theta=\pi+\arctan\left(\frac{-0.075}{78.69}\right)$
and $|-78.69+0.075i|=78.697$.
Go from there.
• Sep 13th 2011, 09:31 AM
nameck
Re: solving comple number
should i apply DeMoivre's Theorem?
• Sep 13th 2011, 09:43 AM
Plato
Re: solving comple number
Quote:

Originally Posted by nameck
should i apply DeMoivre's Theorem?

$\sqrt{78.697}\cdot\exp\left(\frac{\theta i}{2}\right)$