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Chapter 6: Problem 6

Plot each complex number and find its absolute value. $$z=2+5 i$$

Short Answer

Expert verified
The point representing the complex number \(z=2+5i\) is (2, 5) in the complex plane. The absolute value of \(z\) is \(\sqrt{29}\).

Step by step solution

01

Identify the Real and Imaginary Parts of the Complex Number

For the complex number \(z=2+5i\), the real part is \(Re(z) = 2\) and the imaginary part is \(Im(z) = 5\). These values will be used to plot the complex number on the complex plane.
02

Plot the Complex Number

Plot the point (2, 5) in the complex plane (also known as Argand plane). The x-coordinate corresponds to the real part of the complex number (2) and the y-coordinate corresponds to the imaginary part of the complex number (5).
03

Calculate the Absolute Value of the Complex Number

The absolute value (or modulus) of a complex number is given by the formula \(\sqrt{a^2+b^2}\). By substituting \(a = 2\) and \(b = 5\) into the formula, we get \(\sqrt{2^2+5^2} = \sqrt{29}\).

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Most popular questions from this chapter

Use a graphing utility to graph \(r=1+2 \sin n \theta\) for \(n=1,2,3,4,5,\) and \(6 .\) Use a separate viewing screen for each of the six graphs. What is the pattern for the number of large and small petals that occur corresponding to each value of \(n\) ? How are the large and small petals related when \(n\) is odd and when \(n\) is even?

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