W16 - HW Solutions

01

(a) Use Euler’s Formula:

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(b)

02

(The point is in Quadrant II, which is UNSAFE.)

So the polar form is:

The exponential form is:

03

For roots, always start by writing in exponential:

Now use the roots formula:

Write out these roots by evaluating at :

04

(a)

(The point is in Quadrant IV, which is SAFE.)

So the polar form is:

The exponential form is:

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(b)

This one is easy:

05

(a)

Product:

Dividend:

Reciprocal:

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(b)

Product:

Dividend:

Reciprocal:

06

(a)

Convert to polar:

De Moivre’s Theorem:

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(b)

Convert to polar:

De Moivre’s Theorem:

07

(a)

For roots, always start by writing in exponential:

Now use the roots formula:

Write out these roots by evaluating at :

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(b)

For roots, always start by writing in exponential:

Now use the roots formula:

Write out these roots by evaluating at :

(The polar answers are acceptable too.)