Write the complex number in trigonometric form r(c $$r ( \cos \theta + i \sin \theta )$$ ), with $$\theta$$ in the interval [0 $$\left[ 0 ^ { \circ } , 360 ^ { \circ } \right)$$
-$- \sqrt { 7 } - i \sqrt { 7 }$
A) $\sqrt { 14 } \left( \cos 225 ^ { \circ } + i \sin 225 ^ { \circ } \right)$
B) $\sqrt { 14 } \left( \cos 315 ^ { \circ } + i \sin 315 ^ { \circ } \right)$
C) $\sqrt { 14 } \left( \cos 135 ^ { \circ } + i \sin 135 ^ { \circ } \right)$
D) $\sqrt { 14 } \left( \cos 45 ^ { \circ } + \mathrm { i } \sin 45 ^ { \circ } \right)$

Question

Quizplus · Accepted Answer

The complex number $- \sqrt { 7 } - i \sqrt { 7 }$ has a magnitude $r = \sqrt{(-\sqrt{7})^2 + (-\sqrt{7})^2} = \sqrt{14}$ and an angle $\theta = 225^\circ$ because it lies in the third quadrant where both real and imaginary parts are negative.

Write the Complex Number in Trigonometric Form R(c r(cos⁡θ+isin⁡θ)r ( \cos \theta + i \sin \theta )r(cosθ+isinθ)

Write the Complex Number in Trigonometric Form R(c $r ( \cos \theta + i \sin \theta )$