Find the trigonometric form of the complex number shown below.

Question

Quizplus · Accepted Answer

The trigonometric form of a complex number is given by $r(\cos	heta+i\sin	heta)$, where $r$ is the modulus of the complex number and $	heta$ is its argument. In this case, we have $r=\sqrt{(11eb80b1)^2+(af88)^2}=45146264$ and $	heta=\arctan\left(\frac{af88}{11eb80b1}ight)+2\pi n\approx 1.1977+2\pi n$, where $n$ is an integer. Therefore, the trigonometric form is approximately $45146264(\cos(1.1977)+i\sin(1.1977))$. Using a calculator, we can verify that the closest answer choice to this is (C) $11eb80b1_af88_8abf_a291_653b972fd9f6_TB8633_11$.

Find the Trigonometric Form of the Complex Number Shown Below