# Math Help - complex numbers question help

1. ## complex numbers question help

can someone tell me where i have gone wrong i am stuck on this last question, i am pretty sure i have done something wrong:

I have to do product over sum to combine the two equations

Z1 X Z3
-------
Z1 + Z3

Z1=10+J30 Z3=2-J20

Z1= 31.6 <71.5 degrees
Z3= 20 <84.2 degrees

(31.6<71.5)(20<84.2) 632<155.7
--------------------- = ------------
(10+J30)+(2-J20) 12+j10

-576 + J260
= ------------
12 + J10

(-576+J260)(12-J10)
= ---------------------
(12+J10)(12-J10)

-6912+J5760+3120-J2600
= -------------------------
144-120J+120J-J^2 100

-3792 + J3160
= ---------------
144-100

Have i gone wrong as this does not seem correct?

2. Yeah, you've made a mistake in there somewhere. I would advise against going to the polar representation to do the multiplication, as the trig functions have ambiguities. You can do the multiplication in rectangular coordinates. Just foil it out, and use $j^{2}=-1.$ What do you get?