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Chapter 2: Problem 1

Add or subtract as indicated and write the result in standard form. $$(7+2 i)+(1-4 i)$$

Short Answer

Expert verified
The sum of complex numbers \(7+2i\) and \(1-4i\) is \(8-2i\).

Step by step solution

01

Identify the Real and Imaginary Parts

The first step in adding complex numbers is to identify the real and imaginary parts separately. Here, in the first complex number \(7+2i\), 7 is the real part and 2 is the imaginary part. In the second complex number \(1-4i\), 1 is the real part and -4 is the imaginary part.
02

Add the Real Parts

After identifying the real parts of both complex numbers, add them together. The real parts are 7 and 1. Add 7 + 1 to get the real component of the resultant complex number, which is 7 + 1 = 8.
03

Add the Imaginary Parts

Same like the real parts, add the imaginary parts of both complex numbers. The imaginary parts are 2 and -4. Add these together to get the imaginary part of the resultant complex number, which is 2 + -4 = -2.
04

Write the answer in Standard Form

Now combine the real part (8) and the imaginary part (-2) to give the final answer in standard form, which is \(8 - 2i\).

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