Complex Numbers
What is Complex Numbers ?
Complex numbers extend real numbers with an imaginary part, written as a + bi. They represent quantities with both real and imaginary components. Complex numbers have properties and operations such as addition, subtraction, multiplication, and division. They can be visualized in the complex plane. Complex numbers are used in solving equations, studying physics and engineering, and representing complex data. Understanding complex numbers is essential for advanced mathematics and scientific applications.
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Table of Content
1. Introduction.
2. Real & Imaginary parts of a complex number.
\3. Algebraic operation with complex numbers.
4. Equality of two complex number.
5. Conjugate of a complex number.
6. Modulus of complex number.
7. Argument of a complex number.
8. Square root of a complex number.
9. Representation of complex number.
10. Logarithm of a complex number.
11. Geometry of a complex number.
12. Use of complex numbers in co-ordinate geometry.
13. Rotation theorem.
14. Triangle inequalities.
15. Standard loci in the argand plane.
16. De’ moivre's theorem.
17. Roots of complex number.
18. Shifting the origin in case of complex numbers.
19. Inverse points.
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