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:

Kenneth S. answered • 06/02/17

Tutor
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Elle G.

Thank you Kenneth! I'm not sure I'll ever really understand polar coordinates and representation but this helps a lot. 
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06/02/17

Arturo O.

Elle,
 
In general, when given a complex number 
 
z = x + iy,
 
the polar form is
 
z = re
 
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
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06/02/17

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