Elle G.

asked • 06/02/17

Trig Question: What is the polar representation of z = 6i?

What is the polar representation of z = 6i?
 
a. 6cis i
b. 6 cis π
c. π cis 6
d. 6cis (π/2)
e. 36
 
I cant seem to figure this one out

1 Expert Answer

By:

Inactive Tutor answered • 06/02/17

Tutor
New to Wyzant

See tutors like this
See tutors like this
d, because the magnitude is 6 and the angle is pi/2 (90deg) which aims you along the Imaginary (vertical) axis in the Argand plane where complex numbers are represented.
Upvote • 0 Downvote
More
Report

Elle G.

Thank you Kenneth! I'm not sure I'll ever really understand polar coordinates and representation but this helps a lot. 
Report

06/02/17

Inactive Tutor

Elle,
 
In general, when given a complex number 
 
z = x + iy,
 
the polar form is
 
z = reiφ
 
where
 
r = √(x2 + y2)  [always positive]
φ = tan-1(y/x)  [Be careful with your selection of the quadrant for φ!]
 
But if x = 0 (as in your posted problem), then
 
z = yeiπ/2
 
This is true because the polar representation of i is 
 
i = eiπ/2 = cos(π/2) + i sin(π/2) = 0 + i(1) = i
Report

06/02/17

DAVID A.

If an ant is 100 feet away from a tree growing straight up, and the ant has to look up at an angle of 68 degrees to see the top of the tree, how tall is the tree? Select the closest answer.
Report

08/14/21

Still looking for help? Get the right answer, fast.

Ask a question for free

Get a free answer to a quick problem.
Most questions answered within 4 hours.

OR

Find an Online Tutor Now

Choose an expert and meet online. No packages or subscriptions, pay only for the time you need.