The complex number -5i has the complex trigonometric form of 5(cos 270o + isin 270o) Determine if the statement given is true or false.

TRUE

Step-by-step explanation:

A complex number is represented as z = x + iy

Given the complex number -5i, this can also be written as;

z = 0-5i

Get the modulus

|z| = √0²+(-5)²

|z| = √25

|z| = 5

Get the argument

theta = arctan(y/x)

theta = arctan(-5/0)

theta = arctan(-∞)

theta = -90degrees

Since tan is negative in the 2nd and fourth quadrant

in the fourth quadrant, theta - 360 - 90

theta = 270 degrees

Express in polar form;

z = |z|(cos theta + i sintheta)

z = 5(cos270°+ison270°)

Hence the statement given is TRUE

truue

Step-by-step explanation:

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