Find the trigonometric form of the complex number shown below.

Question

Quizplus · Accepted Answer

To find the trigonometric form of a complex number, we need to find the magnitude and argument of the number. The magnitude is the distance from the origin to the point representing the complex number in the complex plane, and the argument is the angle between the positive real axis and the line connecting the origin and the point representing the complex number.

To find the magnitude, we use the Pythagorean theorem:

|11eb80b1_af91_64ee_a291_697588ab317d_TB8633_11| = sqrt((11eb80b1)^2 + (af91)^2)

|11eb80b1_af91_64ee_a291_697588ab317d_TB8633_11| = sqrt(1562a9d9cd6a + ea21)

|11eb80b1_af91_64ee_a291_697588ab317d_TB8633_11| = sqrt(1562a9d9cd6b)

|11eb80b1_af91_64ee_a291_697588ab317d_TB8633_11| = 3c238

To find the argument, we use the inverse tangent function:

arg(11eb80b1_af91_64ee_a291_697588ab317d_TB8633_11) = arctan(af91/11eb80b1)

arg(11eb80b1_af91_64ee_a291_697588ab317d_TB8633_11) = arctan(0.0100)

arg(11eb80b1_af91_64ee_a291_697588ab317d_TB8633_11) = 0.5729 radians = 32.84 degrees

Therefore, the trigonometric form of the complex number is:

3c238(cos(32.84) + i sin(32.84))

This corresponds to choice C.

Find the Trigonometric Form of the Complex Number Shown Below