SOLUTION: Evaluate: 7*((cos( π/3)+isin( π/3))/√3(cos( π/6) +isin(π/6))) thanks.

Algebra ->  Trigonometry-basics -> SOLUTION: Evaluate: 7*((cos( π/3)+isin( π/3))/√3(cos( π/6) +isin(π/6))) thanks.      Log On


   



Question 982566: Evaluate:
7*((cos( π/3)+isin( π/3))/√3(cos( π/6) +isin(π/6)))
thanks.

Answer by AnlytcPhil(1806) About Me  (Show Source):
You can put this solution on YOUR website!


To divide two complex numbers in polar form you divide the numbers 
out front (the absolute values) and subtract the angles.
 
So divide the 7 by sqrt%283%29 and subtract pi%2F3-pi%2F6



Rationalize the denominator and simplify pi%2F3-pi%2F6=2pi%2F6-pi%2F6=pi%2F6

expr%287sqrt%283%29%2F3%29%2A%28cos%28pi%2F6%29%5E%22%22%2Bi%2Asin%28pi%2F6%29%29

If you want that out of trig form, then replace the cosine and sine by
their values

expr%287sqrt%283%29%2F3%29%2A%28sqrt%283%29%2F2%2Bi%2Aexpr%281%2F2%29%29%29
 


7%2A3%2F6%2Bexpr%287sqrt%283%29%2F6%29i

7%2F2%2Bexpr%287sqrt%283%29%2F6%29i

Edwin