Find the trigonometric form of - 21 - 21i.
A) $\frac { 21 } { 2 } \left( \cos \frac { 5 \pi } { 2 } + i \sin \frac { 5 \pi } { 2 } \right)$
B) $21 \left( \cos \frac { 5 \pi } { 2 } + i \sin \frac { 5 \pi } { 2 } \right)$
C) $21 \left( \cos \frac { 5 \pi } { 4 } + i \sin \frac { 5 \pi } { 4 } \right)$
D) $21 \sqrt { 2 } \left( \cos \frac { 5 \pi } { 4 } + i \sin \frac { 5 \pi } { 4 } \right)$
E) $\frac { 441 } { 4 } \left( \cos \frac { 5 \pi } { 8 } + i \sin \frac { 5 \pi } { 8 } \right)$

Question

Find the trigonometric form of - 21 - 21i.  
A) $\frac { 21 } { 2 } \left( \cos \frac { 5 \pi } { 2 } + i \sin \frac { 5 \pi } { 2 } \right)$
B)  $21 \left( \cos \frac { 5 \pi } { 2 } + i \sin \frac { 5 \pi } { 2 } \right)$
C)  $21 \left( \cos \frac { 5 \pi } { 4 } + i \sin \frac { 5 \pi } { 4 } \right)$
D)  $21 \sqrt { 2 } \left( \cos \frac { 5 \pi } { 4 } + i \sin \frac { 5 \pi } { 4 } \right)$
E)  $\frac { 441 } { 4 } \left( \cos \frac { 5 \pi } { 8 } + i \sin \frac { 5 \pi } { 8 } \right)$

Quizplus · Accepted Answer

The trigonometric form of a complex number $z = r(\cos \theta + i\sin \theta)$, where $r = |z| = \sqrt{a^2 + b^2}$ and $\theta = \arg(z)$. For $-21 - 21i$, $r = \sqrt{(-21)^2 + (-21)^2} = 21\sqrt{2}$ and $\theta = \frac{5\pi}{4}$ because the point is in the third quadrant where both sine and cosine are negative. Thus, the correct form is $21\sqrt{2}(\cos\frac{5\pi}{4} + i\sin\frac{5\pi}{4})$.

Find the Trigonometric Form of - 21 - 21i 212(cos⁡5π2+isin⁡5π2)\frac { 21 } { 2 } \left( \cos \frac { 5 \pi } { 2 } + i \sin \frac { 5 \pi } { 2 } \right)221​(cos25π​+isin25π​)

Find the Trigonometric Form of - 21 - 21i $\frac { 21 } { 2 } \left( \cos \frac { 5 \pi } { 2 } + i \sin \frac { 5 \pi } { 2 } \right)$