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Polar Coordinates

Polar coordinates are a way to describe where a point is on a plane. Instead of using x and y, you use the angle theta and radius r, to describe the angle and distance of the point from the origin.

Level 3

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?

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?

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

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

\[ \large \ln {( i) } = \ ?\]

What do we obtain when we multiply the polar coordinates:

\[ ( r_1 , \theta _1 ) \times ( r_2 , \theta _2 ) ? \]

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