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Algebra

Polar Coordinates

Concept Quizzes

Polar Coordinates Warmup
Converting Polar Coordinates to Cartesian
Converting Cartesian Coordinates to Polar
Polar Coordinates - Convert Functions
Polar Coordinates - Complex Numbers
Polar Coordinates - Multiplication
Polar Coordinates - Problem Solving

Challenge Quizzes

Polar Coordinates: Level 3 Challenges
Polar Coordinates: Level 4 Challenges

Polar Coordinates: Level 3 Challenges

If the center of a regular hexagon is at the origin and one of the vertices on the Argand plane is $1 + 2i$ , then what is its perimeter?

2\sqrt { 5 }

6\sqrt{5}

4\sqrt { 5 }

5\sqrt { 5 }

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by Gaurav Adusumilli

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The Nautilus Spiral is given by the polar coordinates $r = e ^ \theta$ . Its shape resembles that of the Nautilus Shell, hence its name.

Which of the following statements about this curve is false?

The curve is self-similar. The half-line

\theta=\alpha

is cut into lengths which form a geometric progression. The distance along the curve from the origin to the point

\theta=0

is infinite. The curve from

\theta=-\infty

\theta=0

loops around the origin infinitely many times.

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by Chung Gene Keun

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$\large \ln\left(\dfrac{\omega^\omega}{\omega^{\omega^2}}\right)$

If $\omega$ is a non-real complex cube root of unity, then what is the value of the expression above?

\dfrac{\pi}{3}

\dfrac{\pi}{\sqrt3}

\dfrac{-2\pi}{\sqrt3}

\dfrac{-2\pi}{3}

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by Parag Zode

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$\large \ln {( i) } = \ ?$

\pi

{e}^{i}

Undefined

\frac{1}{2}i\pi

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by Michael Fuller

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What do we obtain when we multiply the polar coordinates:

$( r_1 , \theta _1 ) \times ( r_2 , \theta _2 ) ?$

( r_1 \times r_2 , \theta_1 \times \theta _2 )

( r_1 + r_2 , \theta_1 \times \theta _2 )

( r_1 + r_2 , \theta_1 + \theta _2 )

( r_1 \times r_2 , \theta_1 + \theta _2 )

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by Calvin Lin

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