Write the complex number shown below in trigonometric form.

Question

Quizplus · Accepted Answer

To convert a complex number from rectangular form to trigonometric form, we can use the following formulas:

Magnitude: |z| = sqrt(Re(z)^2 + Im(z)^2)
Argument: arg(z) = arctan(Im(z)/Re(z)) + k*2pi (where k is an integer and we add multiples of 2pi to account for the angle being on a unit circle).

Plugging in the values from the given complex number, we have:

Re(z) = 11ea cce6 1f5d 651f
Im(z) = 9f49 39a2 6102 08e0

|z| = sqrt((11eacce6_1f5d_651f)^2 + (9f4939a2_6102_08e0)^2) = 11eacce6_1f5d_b241

arg(z) = arctan((9f4939a2_6102_08e0)/(11eacce6_1f5d_651f)) + k*2pi
arg(z) = 2.1318 radians + k*2pi

Then, we can express the complex number in trigonometric form as:

z = |z|(cos(arg(z)) + i sin(arg(z)))
z = 11eacce6_1f5d_b241(cos(2.1318 + k*2pi) + i sin(2.1318 + k*2pi))

The only answer choice that matches this format is C.

Write the Complex Number Shown Below in Trigonometric Form