SaiBook.us Algebra

Lesson Example Discussion Quiz: Class Homework

Lesson

Title: Addition and Subtraction of complex numbers

Grade: 8-b Lesson: S2-L5

Explanation: Hello students, let us learn a new topic in algebra today with definitions, concepts, examples, and worksheets included.

Lesson:

Definition: Complex number

A complex number is the sum of real and imaginary numbers.
A complex number is a number that can be expressed in the form of
a + bi.

$1$

Explanation: Here, the image shows the representation of a complex number. where a and b are real numbers, and i is the imaginary unit with the property that \$ i^2 = - 1\$.

Definition: Addition of Complex Numbers

The addition of complex numbers involves adding their real and imaginary parts separately. If you have two complex numbers a+bi and c+di, their sum is given by:

(a + bi) + (c + di) = (a + c) + (b + d)i

$2$

Explanation: Here’s how it works:

Add the real parts a and c together.
Add the imaginary parts b and d together.
Combine the sums to form the resulting complex number.

Definition: Subtraction of Complex Numbers

Subtraction of complex numbers involves subtracting their real and imaginary parts separately. If you have two complex numbers a+bi and c+di, their sum is given by:

(a + bi) - (c + di) = (a - c) + (b - d)i

$3$

Explanation: Here’s how it works:

Subtract the real part c from a.
Subtract the imaginary part d from b.
Combine the differences to form the resulting complex number.