W16 - Homework

Stepwise problems - Sun. Dec 7, 11:59pm

Complex exponential

01

01

Complex forms - exponential to Cartesian

Write each number in the form .

(a) (b)

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Solution

Solutions---0300-01

02

02

Polar and exponential form

Write down Euler’s Formula.

Now write :

(i) in polar form (ii) in exponential form

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Solution

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Complex roots

03

01

Complex roots using polar

Find the three cube () roots of .

Write your answer in the form .

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Solution

Solutions---0310-01

Regular problems - Tue. Dec 9, 11:59pm

Complex exponential

04

03

Polar and exponential form

Write down Euler’s Formula.

Now write each of the following complex numbers (i) in polar form, and (ii) in exponential form.

(a) (b)

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Solution

Solutions---0300-03

05

04

Complex products and quotients using polar

For each pair of complex numbers and , compute:

(a)

(b)

(Use polar forms with .)

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Solution

Solutions---0300-04

06

05

Complex powers using polar

Using De Moivre’s Theorem, write each number in the form .

(a) (b)

(First convert to polar/exponential, then compute the power, then convert back.)

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Solution

Solutions---0300-05

Complex roots

07

02

Complex roots using polar

Find each of the indicated roots.

(a) The four roots of .

(b) The three cube () roots of .

Try to write your answer in form if that is not hard, otherwise leave it in polar form.

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Solution

Solutions---0310-02