SOLUTION: WRITE THE FOLLOWING COMPLEX NUMBERS IN POLAR FORM: Sqrt{{7}}+sqrt{{21}}*i

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: WRITE THE FOLLOWING COMPLEX NUMBERS IN POLAR FORM: Sqrt{{7}}+sqrt{{21}}*i       Log On


   

Question 1170503: WRITE THE FOLLOWING COMPLEX NUMBERS IN POLAR FORM:
Sqrt{{7}}+sqrt{{21}}*i
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!

Given rectangular form

x%2By%2Ai

the polar form is



where arctan%28y%2Fx%29 is taken in the same quadrant as x%2Byi.

--------------------------------------------------------------------

Given rectangular form

sqrt%287%29%2Bsqrt%2821%29%2Ai, which is in the first quadrant,

the polar form is



where the arctan is taken in the first quadrant.

--------------------------------------------------------------------

Simplifying





Since sqrt%2828%29=sqrt%284%2A7%29=sqrt%284%29%2Asqrt%287%29=2sqrt%287%29

and arctan%28sqrt%283%29%29 in the first quadrant is pi%2F3

Answer:

2sqrt%287%29%28cos%28pi%2F3%29%5E%22%22%2Bi%2Asin%28pi%2F3%29%29

Edwin