Solve the equation. $x ^ { 2 } - i = 0$
A) $- \sqrt { 2 } / 2 - \sqrt { 2 } i / 2 , \sqrt { 2 } / 2 + \sqrt { 2 } i / 2$
B) $- \sqrt { 2 } - 2 i , \sqrt { 2 } + 2 i$
C) $0 - \sqrt { 2 } i / 2,0 + \sqrt { 2 } i / 2$
D) $- 1 - 2 i , 1 + 2 i$
E) $- i , i$

Question

Quizplus · Accepted Answer

To solve $x^2 - i = 0$, add $i$ to both sides to get $x^2 = i$. The solutions to this equation are the square roots of $i$, which can be represented in polar form as $e^{i\pi/4}$ and $e^{i5\pi/4}$ or, equivalently, in rectangular form as $\sqrt{2}/2 + \sqrt{2}i/2$ and $-\sqrt{2}/2 - \sqrt{2}i/2$.

Solve the Equation x2−i=0x ^ { 2 } - i = 0x2−i=0

Solve the Equation $x ^ { 2 } - i = 0$