W15 - Homework

Stepwise problems - Mon. Dec 1, 11:59pm

Complex algebra

01

01

Complex arithmetic

Write each of these expressions in the form .

(a) (b)

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Solution

Solutions---0290-01

02

02

Complex solutions of quadratic equations

Find all solutions and write them in the form .

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Solution

Solutions---0290-02

Regular problems - Thu. Dec 4, 11:59pm

Calculus with polar curves

03

03

Polar curve - Slope of tangent line

Find the slope of the tangent line to the given polar curve:

Hint: First determine parametric Cartesian coordinate functions using as the parameter.

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Solution

Solutions---0280-03

04

04

Polar coordinates - lunar areas

(a) Find the area of the green region.

(b) Find the area of the yellow region.

(You can find these in either order.)

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Solution

Solutions---0280-04

05

05

Pickup region of a microphone - limaçon area

The pickup region of a microphone is described by a limaçon with equation , and part of the region is on a stage.

Find the area of the part of the region on the stage.

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Solution

Solutions---0280-05

06

02

Arclength of one loop of a rose

Consider the graph of the polar curve .

Set up an integral which computes the arclength of one loop of this curve.

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Solution

Solutions---0280-02

07

06

Area of an inner loop

A limaçon is given as the graph of the polar curve .

Find the area of the inner loop of this limaçon.

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Solution

Solutions---0280-06

Complex algebra

08

03

Complex arithmetic

Write each of these expressions in the form .

(a) (b)

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Solution

Solutions---0290-03

09

04

Complex solutions of quadratic equations

Find all solutions and write them in the form .

(a) (b)

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Solution

Solutions---0290-04