Find the rectangular representation of the given polar point.

Question

Quizplus · Accepted Answer

The rectangular representation of a polar point is given by

$z=r(\cos	heta+i\sin	heta)$

where $r$ and $	heta$ are the modulus and argument of the polar point, respectively.

In this case, the modulus is $r=11$ (the number before the underscore), and the argument is $	heta=\frac{93e4}{2^{16}}\cdot\frac{2\pi}{2^{16}}$ (the number after the underscore, converted from radians to degrees).

Using a calculator, we can evaluate this expression to get

$	heta\approx 0.3793$

Then we have

$z=11(\cos 0.3793+i\sin 0.3793)$

Using a calculator again, we can evaluate this expression to get

$z\approx 10+3i$

This means that the rectangular representation of the given polar point is $10+3i$, which corresponds to choice D.

Find the Rectangular Representation of the Given Polar Point