# How do you write the complex number in trigonometric form #4i#?

##### 1 Answer

4i=4 cis (pi/2).

For the general form,

4i = 4 cis ((2k+1/2)pi)

#### Explanation:

Any complex number in rectangular cartesian form is

z = (x, y) = (real part) x + (imaginary part ) iy), where x and y are real.

(x, y) in polar form is

=r cis

The conversion is from

Here, x = 0, y = 4, and so,

The value of theta =

The general value is

All values point to the same direction..

So, seemingly, the general form might be viewed as irrelevant. Yet,

for rotation problems, with

is reached in a cycle of period

Answer: 4i=4 cis (pi/2).

For the general form,

4i = 4 cis ((2k+1/2)pi)