SaiBook.us Algebra

Lesson Example Discussion Quiz: Class Homework

Example

Title: Addition and Subtraction of complex numbers

Grade: 8-b Lesson: S2-L5

Explanation: The best way to understand algebra is by looking at some examples. Take turns and read each example for easy understanding.

Examples:

Perform the following operations with the given complex numbers (3 + 2i) and (1 + 4i):

1. Add the complex numbers.
2. Subtract the second complex number from the first one.

Step 1a

Write down the expression for addition:
(3 + 2i) + (1 + 4i)

Group the real parts and the imaginary parts separately:
(3 + 1) + (2i + 4i)

Add the real parts:
3 + 1 = 4

Add the imaginary parts:
2i + 4i = 6i

Combine the results:
4 + 6i

So, the result of the addition is 4 + 6i.

Explanation: To add the complex numbers (3 + 2i) and (1 + 4i), we combine the real parts and the imaginary parts separately, resulting in (3 + 1) + (2i + 4i). This simplifies to 4 + 6i.

Step 1b

Write down the expression for subtraction:
(3 + 2i) − (1 + 4i)

Distribute the negative sign:
3 + 2i − 1 − 4i

Group the real parts and the imaginary parts separately:
(3 − 1) + (2i − 4i)

Subtract the real parts:
3 − 1 = 2

Subtract the imaginary parts:
2i − 4i = −2i

Combine the results:
2 − 2i

So, the result of the subtraction is 2 − 2i.

Explanation: To subtract (1 + 4i) from (3 + 2i), we subtract the real parts and the imaginary parts separately, resulting in (3 − 1) + (2i − 4i). This simplifies to 2 − 2i.