Exam 40: Trigonometric Form of a Complex Number

Multiply the complex numbers below and leave the result in trigonometric form. $\left[ 7 \left( \cos \frac { 6 \pi } { 7 } + i \sin \frac { 6 \pi } { 7 } \right) \right] \left[ 2 \left( \cos \frac { 4 \pi } { 9 } + i \sin \frac { 4 \pi } { 9 } \right) \right]$

Represent the complex number graphically,and find the trigonometric form of the number.​ $6 + 6 i$ ​

Find the trigonometric form of the complex number shown below. $\sqrt { 3 } + i$

Use the formula to find the missing quantity for the given conditions.The formula E=IZ where E represents voltage,I represents current,and Z represents impedance (a measure of opposition to a sinusoidal electric current),is used in electrical engineering.The variable is a complex number.​ I=13+5i Z=4+3i ​

Find the trigonometric form of - 21 - 21i. ​

Plot the complex number and find its absolute value. ​ -3 + 9i ​

Write the complex number in trigonometric form.​ ​

Write the complex number in trigonometric form.​ ​

Perform the operation and leave the result in trigonometric form.​ $\left( \cos 80 ^ { \circ } + i \sin 80 ^ { \circ } \right) \left( \cos 330 ^ { \circ } + i \sin 330 ^ { \circ } \right)$ ​

Write the complex number shown below in trigonometric form.

Perform the operation shown below and leave the result in trigonometric form. $\left[ 4 \left( \cos \frac { 5 \pi } { 6 } + i \sin \frac { 5 \pi } { 6 } \right) \right] \left[ 3 \left( \cos \frac { 5 \pi } { 6 } + i \sin \frac { 5 \pi } { 6 } \right) \right]$

Represent the complex number below graphically. -3+ 3i

Perform the operation shown below and leave the result in trigonometric form. $\left[ 4 \left( \cos \frac { 2 \pi } { 3 } + i \sin \frac { 2 \pi } { 3 } \right) \right] \left[ 3 \left( \cos \frac { 3 \pi } { 7 } + i \sin \frac { 3 \pi } { 7 } \right) \right]$

​Find the trigonometric form of the complex number shown below. ​ -7 - i

Divide the complex numbers below and leave the result in trigonometric form. $\frac { 10 \left( \cos 220 ^ { \circ } + i \sin 220 ^ { \circ } \right) } { 7 \left( \cos 210 ^ { \circ } + i \sin 210 ^ { \circ } \right) }$

Represent the complex number graphically,and find the trigonometric form of the number. ​ -8i ​

Find the trigonometric form of the complex number shown below. ​ -6i

Represent the complex number graphically,and find the trigonometric form of the number. ​ 12i ​

Perform the indicated operation using the standard form.​ $( 2 + 2 i ) ( 1 - i )$ ​

Find the trigonometric form of $- 9 + 9 i$ .