Find the trigonometric form of the complex number shown below. $- 3 + 4 i$
A) $\sqrt { 25 }$ (cos (arctan (- $\frac { 1 } { 6 }$ )) + i sin (arctan (- $\frac { 1 } { 6 }$ )))
B) $\sqrt { 25 }$ (cos (arctan ( $\frac { 4 } { 5 }$ )) + i sin (arctan ( $\frac { 4 } { 5 }$ )))
C) $\sqrt { 25 }$ (cos (arctan (- $\frac { 4 } { 3 }$ )) + i sin (arctan (- $\frac { 4 } { 3 }$ )))
D) $\sqrt { 25 }$ (cos (arctan (- $\frac { 2 } { 3 }$ )) + i sin (arctan (- $\frac { 2 } { 3 }$ )))
E) $\sqrt { 25 }$ (cos (arctan (4)) + i sin (arctan (4)))

Question

Find the trigonometric form of the complex number shown below.   $- 3 + 4 i$  
A)  $\sqrt { 25 }$ (cos (arctan (- $\frac { 1 } { 6 }$ )) + i sin (arctan (- $\frac { 1 } { 6 }$ )))
B)  $\sqrt { 25 }$ (cos (arctan ( $\frac { 4 } { 5 }$ )) + i sin (arctan ( $\frac { 4 } { 5 }$ )))
C)  $\sqrt { 25 }$ (cos (arctan (- $\frac { 4 } { 3 }$ )) + i sin (arctan (- $\frac { 4 } { 3 }$ )))
D)  $\sqrt { 25 }$ (cos (arctan (- $\frac { 2 } { 3 }$ )) + i sin (arctan (- $\frac { 2 } { 3 }$ )))
E)  $\sqrt { 25 }$ (cos (arctan (4)) + i sin (arctan (4)))

Quizplus · Accepted Answer

The modulus of the complex number $-3 + 4i$ is $\sqrt{(-3)^2 + 4^2} = \sqrt{25} = 5$. The argument is $\arctan\left(\frac{4}{-3}\right)$, which is in the second quadrant, so it is $\pi + \arctan\left(\frac{4}{-3}\right)$. The correct trigonometric form is $5(\cos(\arctan(-\frac{4}{3})) + i\sin(\arctan(-\frac{4}{3})))$.

Find the Trigonometric Form of the Complex Number Shown Below −3+4i- 3 + 4 i−3+4i

Find the Trigonometric Form of the Complex Number Shown Below $- 3 + 4 i$