Question

How do you simplify `6[cos(-pi/3)+isin(-pi/3)]*3(cos((5pi)/6)+isin((5pi)/6))` and express the result in rectangular form?

Answer 1

18i

Explanation:

Using Euler's formula, it would be

`cos(-pi/3) +i sin (-pi/3)= cos(pi/3) -i sin(pi/3)= e^(-ipi/3)`

`cos(5pi/6) +i sin (5pi/6)= e^i (5pi)/6`

The given expression is thus equivalent to `18 e^(-ipi/3)*e^(i (5pi)/6`

= `18 e^(i(-pi/3 +5pi/6)` = `18e^(i pi/2)` = `18[ cos(pi/2)+i sin (pi/2)]`= 18i.