# finding Zc of a long transmission line

#### hunterage2000

Joined May 2, 2010
487
Can someone tell me why my calculator is returning a maths error when I try to find the square root of a complex number and how I do it?

I'm trying to find the value of Zc = the square root of z/y and don't know how to do this manually.

#### t_n_k

Joined Mar 6, 2009
5,455
There may be constraints on the permissible argument range but the simplest way is to use the polar form of the complex number.

The resultant magnitude is the square root of the original magnitude and the resultant phase angle is half the original phase angle.

$$\sqrt{A\angle \theta}=sqrt{A}\angle{\frac{\theta}{2}}$$

#### hunterage2000

Joined May 2, 2010
487
thank you t n k

#### t_n_k

Joined Mar 6, 2009
5,455
The other thing to keep in mind is that some calculators do certain operations differently when the result should be the same.

I use a HP35s Scientific calculator. It handles complex number operations.

Sure enough, if I enter a complex value such as 2+2i and take the square root (using the √x key) I get an error message "Invalid Data".

However, if I enter the same data but use the y^x operation where y is the complex value 2+2i and x=0.5 I get the correct answer without an error. Clearly the calculator uses two different algorithms to perform a task which one would think, gives the same result. Something to be aware of - particularly when the outcome is helpful.