Algebra

# 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?

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

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

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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