Complex Numbers

z = a + i b; a, b \in ℝ, i = \sqrt{- 1}

The modulus of a complex number

r = \sqrt{a^{2} + b^{2}}

The argument of a complex number

t g φ = \frac{b}{a} (a \neq 0)

The real part of the complex number

R e (z) = a = r \cdot \cos φ

The imaginary part of the complex number

I m (z) = b = r \cdot \sin φ

Rectangular form of a complex number

z = a + i b

Polar form of a complex number

z = r \cdot (\cos φ + i \cdot \sin φ)

Exponential form of a complex number

z = r \cdot e^{φ i}

Conjugate of a complex number

z = a + i b = r \cdot (\cos φ + i \cdot \sin φ) = r \cdot e^{φ i}

\bar{z} = a - i b = r \cdot (\cos φ - i \cdot \sin φ) = r \cdot e^{- φ i}

Keywords: Complex Numbers

Polynomials
Special Binomials
Progressions
Arithmetic progression
Geometric progression
Logarithm
Logarithm
Changing the base of a logarithm
Exponents
Powers
Roots
Roots
Proportionality
Direct and Inversely Proportion
Inequalities
Inequalities
Equations
Quadratic equation
Cubic Equations
Irrational and transcendental equations
Complex numbers
Complex Numbers
Adding and Subtracting Complex Numbers
Multiplying and Dividing Complex Numbers
Power of complex numbers
Roots of complex numbers
Kamatni račun
Interest calculation,
Matrices
Definition, adding & subtracting of matrices
Multiplying matrices