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Chapter 11: Problem 25

Explain how to add complex numbers.

Short Answer

Expert verified
To add two complex numbers (a + bi) and (c + di), simply add the real parts (a and c) and the imaginary parts (b and d) separately. The sum will be a new complex number of the form (a+c) + (b+d)i. For example, to add (3+4i) and (-1+2i), we get (3-1) + (4+2)i, which is 2+6i.

Step by step solution

01

Identify the complex numbers

Given two complex numbers, in the form of a + bi and c + di, where a, b, c, and d are real numbers.
02

Add the real parts

Add the real parts (a and c) of the two complex numbers: \(a + c\)
03

Add the imaginary parts

Add the imaginary parts (b and d) of the two complex numbers: \(b + d\)
04

Combine the real and imaginary parts

Combine the sum of the real parts and the sum of the imaginary parts to form a new complex number (a+c) + (b+d)i.
05

Example

Let's add two complex numbers (3+4i) and (-1+2i). First, identify the real parts (3 and -1) and the imaginary parts (4 and 2). Next, add the real parts: \(3+(-1) = 3-1 = 2\) Then, add the imaginary parts: \(4+2 = 6\) Finally, combine the real and imaginary parts to form a new complex number: 2 + 6i

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