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Chapter 6: Problem 3

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

Short Answer

Expert verified
The absolute value of the complex number \(z = 3\) is 3.

Step by step solution

01

Identifying Real and Imaginary Parts

Given the complex number \(z = 3\), it is clear that the real part is 3 and the imaginary part is 0.
02

Plotting the Complex Number

Plot the point at (3, 0) on the complex plane. '3' on the horizontal axis represents the real part and '0' on the vertical axis represents the imaginary part.
03

Calculating the Absolute Value

The absolute value of a complex number \(a + bi\) is given by \(\sqrt{a^2 + b^2}\). So, for \(z = 3\), the absolute value is \(\sqrt{3^2 + 0^2} = 3\).

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Most popular questions from this chapter

Use the dot product to determine whether v and w are orthogonal. $$\mathbf{v}=8 \mathbf{i}-4 \mathbf{j}, \quad \mathbf{w}=-6 \mathbf{i}-12 \mathbf{j}$$

Group members should research and present a report on unusual and interesting applications of vectors.

Explain how to find the dot product of two vectors.

Find \(\text {pro}_{\mathbf{w}} \mathbf{V}\) Then decompose v into two vectors, \(\mathbf{v}_{1}\) and \(\mathbf{v}_{2},\) where \(\mathbf{v}_{1}\) is parallel to \(\mathbf{w}\) and \(\mathbf{v}_{2}\) is orthogonal to \(\mathbf{w}.\) $$\mathbf{v}=3 \mathbf{i}-2 \mathbf{j}, \quad \mathbf{w}=\mathbf{i}-\mathbf{j}$$

I'm working with a unit vector, so its dot product with itself must be 1
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