Polar Coordinates

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+2i1 + 2i , then what is its perimeter?

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

Which of the following statements about this curve is false?

ln(ωωωω2)\large \ln\left(\dfrac{\omega^\omega}{\omega^{\omega^2}}\right)

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

ln(i)= ? \large \ln {( i) } = \ ?

What do we obtain when we multiply the polar coordinates:

(r1,θ1)×(r2,θ2)? ( r_1 , \theta _1 ) \times ( r_2 , \theta _2 ) ?


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