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Chapter 2: Problem 65

Explain how to add complex numbers. Provide an example with your explanation.

Short Answer

Expert verified
The sum of the complex numbers \(3 + 2i\) and \(1 + 4i\) is \(4 + 6i\).

Step by step solution

01

Identify the Real and Imaginary Parts

Given two complex numbers, identify which parts are real and which are imaginary. For example, in the complex numbers \(3 + 2i\) and \(1 + 4i\), \(3\) and \(1\) are the real parts, while \(2i\) and \(4i\) are the imaginary parts.
02

Add the Real Parts

Add the real parts of the two complex numbers together. Using our example, this would be\(3 + 1 = 4\).
03

Add the Imaginary Parts

Next, add the imaginary parts of the two complex numbers together. In our example, this would be \(2i + 4i = 6i\).
04

Combine the Results

Combine the sum of the real parts and the sum of the imaginary parts to get the sum of the complex numbers. In this case, this would give us \(4 + 6i\).

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