Complex numbers

Lecture

A complex number is an expression of the form z = a + bi, where a, b are any real numbers, i is an imaginary unit that satisfies the condition i2 = -1. In this case, denote a = Re z - the real part of the number, b = Im z - the imaginary part of it.

Basic agreements:

The real number a is also written as a + 0i.
Pure imaginary number bi, i.e. 0 + bi.
Two complex numbers z1 = a + bi and z2 = c + di are considered equal if a = c and b = d.

The number z1 = a - bi is called the conjugate number z = a + bi.

Complex numbers

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Часть 1 Complex numbers

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Terms: Algebra

Complex numbers

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Biquaternion

Cayley algebra (octonions or octaves)

Arithmetic operations on complex numbers

Complex plane

Trigonometric form of a complex number

Raising a complex number to a power - example

Extracting a root from a complex number

Solving quadratic equations with complex numbers

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