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Chapter 6: Problem 4

Plot each complex number and find its absolute value. $$z=4$$

Short Answer

Expert verified
The absolute value of the complex number \(z=4\) is 4.

Step by step solution

01

Identify the complex number

First thing to note here is that the complex number provided \(z=4\) is, in fact, a real number. In the realm of complex numbers, it can also be written as \(4 + 0i\), where the real part is 4 and the imaginary part is 0.
02

Plot the complex number

To plot the complex number, treat the real part (4) as the x-coordinate and the imaginary part (0) as the y-coordinate. This is analogous to plotting on an xy plane. Since the y-coordinate here is 0, the point lies on the real (x) axis at point (4,0).
03

Find the absolute value of the complex number

The absolute value of a complex number \(z = a + bi\) is the distance from the origin to the point (a, b) and is denoted by \(\|z\|\), is given by the Pythagorean theorem as \(\sqrt{a^2 + b^2}\). Therefore, the absolute value of \(z=4\) or \(4 + 0i\) is the \(\sqrt{4^2 + 0^2} = 4\).

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