How can you use trigonometric functions to simplify 4 e^( ( 5 pi)/4 i ) into a non-exponential complex number?

1 Answer
Topscooter
Dec 21, 2015

Use the Moivre formula.

Explanation:

The Moivre formula tells us that e^(itheta) = cos(theta) + isin(theta).

Apply this here : 4e^(i(5pi)/4) = 4(cos((5pi)/4) + isin((5pi)/4))

On the trigonometric circle, (5pi)/4 = (-3pi)/4. Knowing that cos((-3pi)/4) = -sqrt2/2 and sin((-3pi)/4) = -sqrt2/2, we can say that 4e^(i(5pi)/4) = 4(-sqrt2/2 -i(sqrt2)/2) = -2sqrt2 -2isqrt2.

Related questions
See all questions in The Trigonometric Form of Complex Numbers
Impact of this question
1514 views around the world
You can reuse this answer
Creative Commons License