153k views
6 votes
The complex number -5i has the complex trigonometric form of 5(cos 270o + isin 270o) Determine if the statement given is true or false.

User Deestan
by
8.9k points

2 Answers

6 votes

Answer:

truue

Explanation:

just did the quiz on edg

User Gavrilo Adamovic
by
8.5k points
8 votes

Answer:

TRUE

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

User Raul Rueda
by
8.2k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories