Write the expression in the standard form a + bi.
-$$\left( - \frac { 1 } { 2 } - \frac { \sqrt { 3 } } { 2 } \mathrm { i } \right) ^ { 10 }$$
A) $\frac { 1 } { 2 } - \frac { \sqrt { 3 } } { 2 } \mathrm { i }$
B) $\frac { 1 } { 2 } + \frac { \sqrt { 3 } } { 2 } \mathrm { i }$
C) $- \frac { 1 } { 2 } - \frac { \sqrt { 3 } } { 2 } \mathrm { i }$
D) $- \frac { 1 } { 2 } + \frac { \sqrt { 3 } } { 2 } \mathrm { i }$

Question

Quizplus · Accepted Answer

The expression is in the form of a complex number in polar form. The magnitude is 1, and the angle is 240 degrees. Raising it to the 10th power results in a rotation of 2400 degrees, which is equivalent to 240 degrees, leading back to the original complex number.

Write the Expression in the Standard Form a + Bi (−12−32i)10\left( - \frac { 1 } { 2 } - \frac { \sqrt { 3 } } { 2 } \mathrm { i } \right) ^ { 10 }(−21​−23​​i)10

Write the Expression in the Standard Form a + Bi $\left( - \frac { 1 } { 2 } - \frac { \sqrt { 3 } } { 2 } \mathrm { i } \right) ^ { 10 }$