Question

help please?? how do i write -3i in trigonometric form?

Answer 1

the complex number \(-i\) is this:

so we have to consider the phase \(\phi=3 \pi/2\)

Answer 2

next, please apply the Euler formula:
\[\large {e^{i\phi }} = \cos \phi + i\sin \phi \]

Answer 3

In other words, starting from the positive real axis, we travel in a circle counterclockwise, passing the positive imaginary axis and the negative real axis, to arrive at the negative imaginary axis.

This counterclockwise motion is described by the angle 3pi/2.

To write -3i in trig form, you'll need to imagine or actually draw a circle of radius ( what? ).

Last step: Describe this destination point in the form (r, theta). r is the radius, theta is the angle. Try it, please.

Answer 4

please replace \(\phi=3 \pi/2\) into both sides of the Euler formula