Write the complex number in trigonometric form. Begin by sketching the graph to help find the argument θ .
B)
C)
D)

Question

Write the complex number in trigonometric form. Begin by sketching the graph to help find the argument θ .  ​
B)​ 
C)​ 
D)​

Quizplus · Accepted Answer

To find the argument θ, we can sketch the complex number on the coordinate plane. The real part is approximately -3 and the imaginary part is approximately 10. Using the Pythagorean theorem, we can find the magnitude to be approximately 10.44. To find the angle, we can use the inverse tangent function:

θ = arctan(10/-3) ≈ -1.294

Since the imaginary part is positive, we know that the angle is in the second quadrant. Thus, we add π radians to get the general angle:

θ = -1.294 + π ≈ 1.847

Finally, we can write the complex number in trigonometric form:

11ebf5ef_bbdf_b0c1_95d1_535b67718564_TBX9354_11 = 10.44(cos 1.847 + i sin 1.847)

Write the Complex Number in Trigonometric Form