Find all solutions of the equation. Leave answers in trigonometric form.
-$$x ^ { 2 } - i = 0$$
A) $\left\{ \operatorname { cis } 180 ^ { \circ } , \operatorname { cis } 0 ^ { \circ } \right\}$
B) $\left\{ \operatorname { cis } 315 ^ { \circ } , \operatorname { cis } 135 ^ { \circ } \right\}$
C) $\left\{ \operatorname { cis } 270 ^ { \circ } , \operatorname { cis } 90 ^ { \circ } \right\}$
D) $\left\{ \operatorname { cis } 45 ^ { \circ } \right.$, cis $\left. 225 ^ { \circ } \right\}$

Question

Quizplus · Accepted Answer

To solve $x^2 - i = 0$, we first isolate $x^2$ to get $x^2 = i$. The complex number $i$ can be represented in trigonometric form as $cis(90^\circ)$ because it lies on the positive imaginary axis. To find the square roots of $i$, we divide the angle by 2 and also consider the angle plus 180 degrees to account for the periodic nature of trigonometric functions. Thus, the solutions are $cis(45^\circ)$ and $cis(225^\circ)$, which correspond to the square roots of $i$ in trigonometric form.

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

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