Engineering Mathematics 13 1 Complex Number Complex Plane
Engineering MathematicsⅡ 제 13 -1 : Complex Number Complex Plane 제 13 -2 : Polar form of Complex Number Powers and Roots
Complex Number Why do we use complex number? History of complex number What is the complex number?
Why do we use complex number?
Complex Number?
Four arithmetical Operations 1. Addition 2. Multiplication
Four Arithematical Operations 3. Substraction 4. Division
Complex Plane Geometrical representation of complex numbers
Geometrical representation of complex numbers
Complex Conjugate Numbers
Polar Form of Complex Numbers (1) (2) (3) (“r” is called the absolute value or modulus of z) (Geometrically |z| is the distance of point z from the origin)
is called the argument of z
Example 1
Polar Form of Complex Numbers Triangle Inequality
We obtain from 6 the generalized triangle inequality ☞ Proof
Reversed triangle Inequality
Polar Form of Complex Numbers Multiplication in polar form
Polar Form of Complex Numbers Division in polar form
De Moivre’s Formula
Roots
Roots
Taking z=1 |z| = r = 1
Example
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