Techniques of complex number
1. Polar form: Representing a complex number in terms of its magnitude and angle in degrees or radians.
2. Cartesian form: Representing a complex number in terms of its real and imaginary components.
3. Conjugation: A complex number's conjugate is created by changing the sign of its imaginary part.
4. Modulus: The magnitude or absolute value of a complex number is given by the square root of the sum of the squares of its real and imaginary components.
5. Exponential form: A complex number can be expressed in exponential form where the real component is the base of e raised to the power of the imaginary component multiplied by i.
6. Addition and subtraction: Complex numbers are added by summing their real and imaginary components separately. Subtraction is performed in the same way.
7. Multiplication and division: Multiplication of complex numbers is performed by distributing one complex number's components across the other complex number's components. Division is performed by multiplying the numerator and denominator by the complex conjugate of the denominator.
8. Argument: The angle between a complex number and the positive real axis is known as the argument.
9. Roots: Finding the nth root of a complex number involves using the polar form, raising the modulus to the 1/n power, and dividing the argument by n.
10. De Moivre's theorem: A theorem that allows us to raise a complex number to a power by using its polar form and applying the angle multiplying property of exponents.