Summary of Complex Number Operations

Different forms

1.    a plus b i, equals r times quantity cosine P plus i sine P, equals r times e to the power i times P, where r squared equals a squared plus b squared, and the tangent of P equals b divided by a, or a equals r times cosine P, and b equals r times sine P

Addition and subtraction

2.    Formula for addition of complex numbers

3.    Formula for subtraction of complex numbers

Multiplication

4.    Formula for multiplication of complex numbers

5.    Trigonometric formula for multiplication of complex numbers

Division

6.    Formula for division of complex numbers

7.    Trigonometric formula for division of complex numbers

Powers and Roots

8.    Formula for powers of complex numbers, for integer values of n.

9.    formula for the nth root of a complex number, for integer values of k and n.

10.    Formula for a complex number to a complex power, where the complex number a plus b i has the trigonometric form cosine P plus i sine P, all times r.

Logarithms

11.    Formula for natural logarithm of a complex number, for integer values of k.

12.    change of base formula for logarithms

Trigonometric functions

13.    Formula for the cosine of a complex number

14.    formula for cosine of a complex number

15.    Formula for the sine of a complex number

16.    formula for sine of a complex number

Hyperbolic functions

17.    Formula for the hyperbolic cosine

18.    formula for hyperbolic cosine of a complex number

19.    Formula for the hyperbolic sine

20.    formula for hyperbolic sine of a complex number

Inverse Trigonometric Functions

21.    Formula for the inverse cosine

22.    Formula for the inverse sine

23.    Formula for the inverse tangent

Inverse Hyperbolic Functions

24.    formula for the inverse hyperbolic cosine

25.    formula for the inverse hyperbolic sine

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