# Form an op w/ three vectors in polar form.

1. Nov 27, 2011

### itlivesthere

1. The problem statement, all variables and given/known data
I'm trying to find the best solution for solving a problem in which I must form an operation with three vectors in polar form, ending with a sum in rectangular form. The operation is as follows:
(5 $\angle$ 0°) + (20 $\angle$ -90°) - (6 $\angle$180°) =

2. Relevant equations
Z1$\angleθ$ + Z2$\angleθ$ = (Z1 + Z2) $\angleθ$, (X1 + jY1) + (X2 + jY2) = (X1 + X2) + j(Y1 + Y2)

3. The attempt at a solution
I tried using the Triangle Law R= (a+b)+(b+c). I'm not sure if I did this correctly or not, but I ended up with this vector in rectangular form: -9 + j1.1*10-15

I'm posting to verify if I did this correctly or if I missed anything.

2. Nov 27, 2011

### cepheid

Staff Emeritus
Welcome to PF,

Although polar form is handy when multiplying complex numbers, rectangular form is far more convenient when adding complex numbers, because you can just add them "component-wise", meaning that you can separately add up their real and their imaginary parts.

So, convert all the numbers to rectangular form. This is trivial here, because, the angles are such that all the numbers lie along one of the coordinate axes.

A phase angle of 0 degrees means that the first number lies along the positive real axis and is just equal to +5

A phase angle of -90 degrees means that the second number lies along the negative imaginary axis and is just equal to -20i

A phase angle of 180 degrees means that the third number lies along the negative real axis and is just equal to -6

+5 + (-20i) - (-6) = 11 - 20i

EDIT: I guess I used the wrong notation. Substitute 'j' whenever you see 'i' above, if it confuses you. They both mean $\sqrt{-1}$.