trigonometry
posted by mikey on .
1) Perform the operation and leave the result in trig. form.
[3/4(cos pi/3 + i sin pi/3)][4(cos 3pi/4 + i sin 3pi/4)]
Thanks

[3/4(cos pi/3 + i sin pi/3)][4(cos 3pi/4 + i sin 3pi/4)]
= (3/4)(1/2 + i (√3/2) (4) (√2/2 + i √2/2)
= (3/4)(1/2)(1 + i √3)(4)(1/2)( √2 + i √2)
= (3/4)(√2 + i√2  i √6 + √6 i^2)
= (3/4) (√2 √6 + i(√2√6) )  in quad III
tan^1  √2√6/√2√6 = 15° or π/12
but the angle is in III , so Ø = 135° or 9π/12
= (3/4)( cos 9π/12 + i sin 9π/12)
check my arithmetic, I should have written it out on paper first.