Exam 40: Trigonometric Form of a Complex Number

Multiply the complex numbers below and leave the result in trigonometric form.​ $\left[ 8 \left( \cos \frac { 2 \pi } { 7 } + i \sin \frac { 2 \pi } { 7 } \right) \right] \left[ 10 \left( \cos \frac { 5 \pi } { 9 } + i \sin \frac { 5 \pi } { 9 } \right) \right]$

Perform the operation shown below and leave the result in trigonometric form. $\left[ 6 \left( \cos 40 ^ { \circ } + i \sin 40 ^ { \circ } \right) \right] \left[ 8 \left( \cos 190 ^ { \circ } + i \sin 190 ^ { \circ } \right) \right]$

​Find the trigonometric form of the complex number shown below.​ $- 3 + 4 i$ ​

Represent the following complex number graphically. ​​ $3 \left( \cos 160 ^ { \circ } + i \sin 160 ^ { \circ } \right)$ ​ ​

Find all solutions to the following equation. $x ^ { 3 } - 8 = 0$ ​

Find the trigonometric form of the complex number shown below. $- 10 i$

Write the complex number in trigonometric form.​ ​

Plot the complex number and find its absolute value. ​ -2 ​

Represent the complex number graphically,and find the trigonometric form of the number. ​ 4 ​

Use DeMoivre's Theorem to find the indicated power of the following complex number. $( - 3 + 3 i ) ^ { 4 }$

Sketch the graph of all complex numbers z satisfying the given condition.​ $| z | = 7$ ​

Find the trigonometric form of $- 18 \sqrt { 3 } - 18$ .

Perform the operation and leave the result in trigonometric form.​ $\frac { 2 \left( \cos 30 ^ { \circ } + i \sin 30 ^ { \circ } \right) } { 3 \left( \cos 120 ^ { \circ } + i \sin 120 ^ { \circ } \right) }$ ​

Find the standard form of the complex number $10 \left( \cos \frac { \pi } { 12 } + i \sin \frac { \pi } { 12 } \right)$ .Round values to the nearest hundredth. ​

Use DeMoivre's Theorem to find the indicated power of the complex number.Write the result in standard form. $\left[ - 5 \left( \cos \left( 210 ^ { \circ } \right) + i \sin \left( 210 ^ { \circ } \right) \right) \right] ^ { 10 }$

Find the standard form of the complex number $6 \left( \cos 17 ^ { \circ } 26 ^ { \prime } + i \sin 17 ^ { \circ } 26 ^ { \prime } \right)$ .Round values to the nearest hundredth. ​

Plot the complex number and find its absolute value. ​ -4i ​

Find the standard form of the complex number.Then represent the complex number graphically.​ $7 ( \cos 0 + i \sin 0 )$ ​

Find the standard form of the complex number $5 \left( \cos \frac { 5 \pi } { 12 } + i \sin \frac { 5 \pi } { 12 } \right)$ .Round values to the nearest hundredth.

Find the cube roots of the following complex number.Write each of the roots in standard form. $27$