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Chapter 6: Problem 2

Plot each complex number and find its absolute value. $$z=3 i$$

Short Answer

Expert verified
The complex number \(3i\) is represented by a point at the coordinates (0,3) in the complex plane. Its absolute value is 3.

Step by step solution

01

Identify the real and imaginary parts

A complex number z can be expressed as \(a + bi\), where 'a' denotes the real part, 'b' denotes the imaginary part and 'i' is the imaginary unit. For our complex number \(3i\), we can see that 'a' = 0 (as there is no real part) and 'b' = 3.
02

Plot the number on the complex plane

On the complex plane, the real part is represented on the horizontal axis and the imaginary part on the vertical axis. Since the real part of our number is 0 and the imaginary part is 3, we plot a point at the coordinates (0,3).
03

Calculate the absolute value of the complex number

The absolute or modulus value of a complex number z = \(a + bi\) is given by \(|z| = \sqrt{a^2 + b^2}\). Therefore, for our number, the absolute value would be \(|3i| = \sqrt{0^2 + 3^2} = 3\).

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