COMPLEX NUMBER

Complex Number

Definition Of Complex Number

Complex Number is a number that can be expressed in the form of x + yi.

More About Complex Number

Complex numbers are numbers that are written as the sum or difference of a real number and an imaginary number.
3 + 5i, 8 - 11i are examples of complex numbers.
Complex Conjugates: The complex numbers a + bi and a - bi are conjugates of each other. We get the conjugate of a complex number just by changing the sign of the imaginary part of the number.
For example, the conjugate of the complex number 12 - 4i is 12 + 4i.

Video Examples: Algebra - Complex Numbers

Solved Example onComplex Number

Ques: Choose the imaginary part of the complex number 10 + 13i.

Choices:

A. 13
B. 13i
C. -10
D. 10
Correct Answer: A

Solution:

Step 1: The imaginary part of a complex number is the coefficient of i in the complex number.
Step 2: So, the imaginary part of the given complex number 10 + 13i is 13.

Quick Summary

Complex numbers combine real and imaginary parts.
They are written in the form a + bi.
Complex conjugates are formed by changing the sign of the imaginary part (a - bi is the conjugate of a + bi).

\[ z = a + bi \]

🍎 Teacher Insights

Use visual aids like the complex plane to help students understand the geometric representation of complex numbers. Emphasize the difference between the imaginary part and the imaginary term. Relate operations with complex numbers to similar operations with binomials.

🎓 Prerequisites

Real Numbers
Basic Algebra

Check Your Knowledge

Q1: What is the imaginary part of the complex number 10 + 13i?

13 13i -10 10

Q2: What is the conjugate of 5 - 2i?

5 + 2i -5 - 2i -5 + 2i 5 - 2i

Frequently Asked Questions

Q: What is the imaginary unit?
A: The imaginary unit, denoted by 'i', is defined as the square root of -1 (i = √-1).

Q: How do you find the conjugate of a complex number?
A: To find the conjugate of a complex number a + bi, simply change the sign of the imaginary part to get a - bi.