Problem 46 - College Algebra

Question

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

Step-by-Step Solution

Answer

The sum of the complex numbers \(4+3i\) and \(2+5i\) is \(6+8i\)

Step 1: Identify the real and imaginary parts

Consider two complex numbers, \(4+3i\) and \(2+5i\). Here, in the first number, the real part is 4 and the imaginary part is 3, and for the second number, the real part is 2 and the imaginary part is 5.

Step 2: Add the real parts

Add the real components from each complex number together. In this case, that gives \(4 + 2 = 6\). This forms the real part of the result.

Step 3: Add the imaginary parts

Next, add together the imaginary components from each complex number. This gives \(3 + 5 = 8\). This forms the imaginary part of the result.

Step 4: Combine the components into one complex number

Combine the real and imaginary components back into a single complex number, taking the form of \(a + bi\). This gives us the final answer, \(6 + 8i\).