How do you simplify #1/2(cos(pi/3)+isin(pi/3))*6(cos((5pi)/6)+isin((5pi)/6))# and express the result in rectangular form?

1 Answer
May 11, 2017

Answer:

To multiply, multiply the magnitudes and add the angles.
Substitute the equivalents for the trigonometric functions.
Use the distributive property.

Explanation:

To multiply, multiply the magnitudes and add the angles.

#1/2(cos(pi/3)+isin(pi/3))*6(cos((5pi)/6)+isin((5pi)/6)) = 3(cos((7pi)/6)+isin((7pi)/6))#

Substitute the equivalents for the trigonometric functions.

#1/2(cos(pi/3)+isin(pi/3))*6(cos((5pi)/6)+isin((5pi)/6)) = 3(sqrt3/2-1/2i)#

Use the distributive property:

#1/2(cos(pi/3)+isin(pi/3))*6(cos((5pi)/6)+isin((5pi)/6)) = (3sqrt3)/2-3/2i#