Problem 59 - Algebra and Trigonometry

Question

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

Step-by-Step Solution

Answer

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

Step 1: Identify the complex numbers

Identify the complex numbers that need to be added. For example, consider the two complex numbers \(3 + 2i\) and \(1 + 4i\).

Step 2: Separate the real and imaginary parts

Separate the real part (the part of the number that doesn't involve \(i\)) and the imaginary part (the part of the number that involves \(i\)) of both complex numbers. For the example numbers, the real parts are 3 and 1, and the imaginary parts are \(2i\) and \(4i\).

Step 3: Add the real parts together

Add the real parts of both numbers together. In this case, 3 (from the first number) plus 1 (from the second number) equals 4.

Step 4: Add the imaginary parts together

Add the imaginary parts of both numbers together. In this case, \(2i\) (from the first number) plus \(4i\) (from the second number) equals \(6i\).

Step 5: State the result

Combine the sum of real and imaginary parts to state the result. This is the answer to the addition of the two complex numbers. Here, the result is \(4 + 6i\), which is the sum of the two complex numbers \(3 + 2i\) and \(1 + 4i\).