Question
Find this quotient. Express the result in rectangular form.
9(cos3π/2 + isin3π/2) ÷ 3(cosπ/4 + isinπ/4)
9(cos3π/2 + isin3π/2) ÷ 3(cosπ/4 + isinπ/4)
Answers
Damon
e^i theta = cos theta + i sin theta
so
9 e^i(3 pi/2)
-----------------
3 e^i(pi/4)
= 3 e^i(5 pi/4)
= 3 [cos (5 pi/4) + i sin (5 pi/4)]
= 3 (-.707) + 3i(-.707)
or
-(3/2) sqrt 2 - (3/2) i sqrt 2
so
9 e^i(3 pi/2)
-----------------
3 e^i(pi/4)
= 3 e^i(5 pi/4)
= 3 [cos (5 pi/4) + i sin (5 pi/4)]
= 3 (-.707) + 3i(-.707)
or
-(3/2) sqrt 2 - (3/2) i sqrt 2