Find all solutions of the equation. Leave answers in trigonometric form.
-$$x ^ { 2 } - 36 = 0$$
A) $\left\{ 6 \sqrt { 2 } \operatorname { cis } 45 ^ { \circ } , 6 \sqrt { 2 } \operatorname { cis } 225 ^ { \circ } \right\}$
B) $\left\{ 6 \sqrt { 2 } \operatorname { cis } 235 ^ { \circ } , 6 \sqrt { 2 } \operatorname { cis } 135 ^ { \circ } \right\}$
C) $\left\{ 6 \operatorname { cis } 180 ^ { \circ } , 6 \operatorname { cis } 0 ^ { \circ } \right\}$
D) $\left\{ 6 \operatorname { cis } 90 ^ { \circ } , 6 \operatorname { cis } 270 ^ { \circ } \right\}$

Question

Quizplus · Accepted Answer

Solving the equation $x^2 - 36 = 0$ gives $x^2 = 36$, which has solutions $x = 6$ and $x = -6$. In trigonometric form, $6$ can be represented as $6\operatorname{cis}0^\circ$ (since $cos(0^\circ) = 1$ and $sin(0^\circ) = 0$), and $-6$ can be represented as $6\operatorname{cis}180^\circ$ (since $cos(180^\circ) = -1$ and $sin(180^\circ) = 0$), reflecting the positive and negative solutions on the real axis.

Find All Solutions of the Equation x2−36=0x ^ { 2 } - 36 = 0x2−36=0

Find All Solutions of the Equation $x ^ { 2 } - 36 = 0$