rectangular form

Question

I am given the following problem:

 

8∠120° + 4∠60°

 

I am given the following instructions: Add. Write answer in rectangular form. Round to one decimal place. Show steps. Use a scientific calculator.

Answer 1

cos(120°) = -1/2

sin(120°) = √(3)/2

 

So, that first portion is equivalent to:

 

r(cosθ + isinθ) = 8(-1/2 + i√(3)/2) = -8/2 + 8i√(3)/2 = -4 + 4i√(3)

 

 

 

cos(60°) = 1/2

sin(60°) = √(3)/2

 

So, that second portion is equivalent to:

 

r(cosθ + isinθ) = 4(1/2 + i√(3)/2) = 4/2 + 4i√(3)/2 = 2 + 2i√(3)

 

 

 

Together, that gives you:

 

-4 + 4i√(3) + 2 + 2i√(3) = -2 + 6i√(3)