1 / 10

Complex Numbers

A First Observation. There is no real number solution to the equation x2 1=0.The square root of 1 is called the imaginary unit and is denoted by i.This provides a solution to x2 1=0, but it is not a real number.. Definition of Complex Number. A complex number z is a number of the form a

kyran
Télécharger la présentation

Complex Numbers

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

    1. Complex Numbers

    2. A First Observation There is no real number solution to the equation x2 + 1=0. The square root of –1 is called the imaginary unit and is denoted by i. This provides a solution to x2+1=0, but it is not a real number.

    3. Definition of Complex Number A complex number z is a number of the form a + bi, where i = ?-1. a is called the real part of z, and b is called the imaginary part of z. The standard form of a complex number is a + bi, where a and b are real numbers.

    4. More on Complex Numbers If b ? 0, z = a + bi is also called an imaginary number. If b = 0, z is a real number. If a = 0 and b ? 0, z is called a pure imaginary number.

    5. Equality of Complex Numbers Two complex numbers a+bi, and c+di are equal if and only if a = c and b = d

    6. Addition and Subtraction of Complex Numbers (a+bi) + (c+di) = (a+c)+(b+d)i (a+bi) – (c+di) = (a-c)+(b-d)i

    7. Multiplication of Complex Numbers (a+bi)(c+di) = (ac-bd)+(ad+bc)i Note that this is simply the first-outer-inner-last rule, and we replace i2 by –1.

    8. Complex Conjugates If z = a+bi, the conjugate of z is a – bi. Note that z and its conjugate are equal if and only if the imaginary part of z = 0, i.e. z is a real number. (a+bi)(a-bi) = a2 + b2

    9. Division of Complex Numbers

More Related