Lesson 10E Complex Polar Planes Solidify Understanding

Ready

Transform point as indicated below.

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  1. Apply the rule to point . Label as

  2. Apply the rule to point . Label as .

  3. Apply the rule to point . Label as .

Point A (4,1) x–5–5–5555y–5–5–5555000

Transform the given graph as indicated below.

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  1. Apply the rule to . Label as .

  2. Apply the rule to . Label as .

  3. Apply the rule to . Label as

Absolute value function opening upwards with vertex (0,0) x–10–10–10–5–5–5555101010y–6–6–6–4–4–4–2–2–2222444666000

Set

Coordinate Conversion:

The polar coordinates are related to the rectangular coordinates as follows:

Graph of triangle with one point as origin, one point as (x,y) (r,theta), vertical component, y and horizontal component, x. OriginPolar axis(x-axis)

Convert the points from polar to rectangular coordinates.

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Convert the points from rectangular to polar coordinates.

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Consider the complex number . The angle is the angle measure from the positive real axis to the line segment connecting the origin and the point . and , where .

By replacing and , you have . Factor out the to obtain the trigonometric form of a complex number.

If , then the trigonometric form is .

Right triangle with vertical component b, horizontal component a, hypotenuse r, point (a,b) and theta, imaginary axis and real axis. real axisimaginary axis

Write the complex numbers in trigonometric form .

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Write the complex number in standard form .

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Go

Use the definition of to find the value of . Recall that has a base of . (NO CALCULATORS)

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