Find Roots of Complex Numbers in Polar Form
-The complex square roots of i (rectangular form)
A) $\frac { \sqrt { 2 } } { 2 } + \frac { \sqrt { 2 } } { 2 } i , - \frac { \sqrt { 2 } } { 2 } - \frac { \sqrt { 2 } } { 2 } i$
B) $\frac { \sqrt { 2 } } { 2 } - \frac { \sqrt { 2 } } { 2 } i , - \frac { \sqrt { 2 } } { 2 } + \frac { \sqrt { 2 } } { 2 } \mathrm { i }$
C) $- 1,1$
D) $- \mathrm { i } , \mathrm { i }$

Question

Quizplus · Accepted Answer

The complex number $i$ has a magnitude of 1 and an angle of $\frac{\pi}{2}$ radians (or 90 degrees) in polar form. To find the square roots, we divide the angle by 2 and find the square root of the magnitude. This gives us two roots at angles of $\frac{\pi}{4}$ and $\frac{5\pi}{4}$ (or 45 and 225 degrees), both with magnitude $\sqrt{1} = 1$. Converting these back to rectangular form gives $\frac{\sqrt{2}}{2} + \frac{\sqrt{2}}{2}i$ and $-\frac{\sqrt{2}}{2} - \frac{\sqrt{2}}{2}i$.

Find Roots of Complex Numbers in Polar Form -The Complex 22+22i,−22−22i\frac { \sqrt { 2 } } { 2 } + \frac { \sqrt { 2 } } { 2 } i , - \frac { \sqrt { 2 } } { 2 } - \frac { \sqrt { 2 } } { 2 } i22​​+22​​i,−22​​−22​​i

Find Roots of Complex Numbers in Polar Form
-The Complex $\frac { \sqrt { 2 } } { 2 } + \frac { \sqrt { 2 } } { 2 } i , - \frac { \sqrt { 2 } } { 2 } - \frac { \sqrt { 2 } } { 2 } i$