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What is the polar form of #( 3,-27 )#?

Answer 1

Aurora Alvarado

#(3sqrt82,- tan^{-1}(9))#

To write in polar form, you need to know

To solve 1. we use Pythagoras Theorem

#r = sqrt{3^2 + (-27)^2}#

#= 3sqrt82#

To solve 2. we first find the quadrant that the point lies in.

#x# is positive while #y# is negative #=># quadrant IV

Then we find the basic angle by taking inverse tangent of #|y/x|#.

#alpha = tan^{-1}(|{-27}/3|)#

#= tan^{-1}(9)#

The angle that we are looking for would be

#theta = -alpha#

#= -tan^{-1}(9)#

#~~ -1.460#

Therefore, the polar coordinate is #(3sqrt82,- tan^{-1}(9))#

Note that the answer above is not unique. You can add any integer multiples of #2pi# to #theta# to get other representations of the same point.

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Answer 2

Paisley Johnson

The polar form of the complex number (3, -27) is 27∠-80.5377° or 27cis(-80.5377°).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.