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# Complex Numbers (redirected from Complex Number and Maclaurin Series)

last edited by 11 years, 3 months ago

Complex Numbers

A complex number is a number, z, which can be put in the form a + bi, where a and b are real numbers and i is called the imaginary unit, where i2 = −1. In this expression, a is called the real part, Re(z), and b the imaginary part, Im(z), of the complex number. Complex numbers extend the idea of the one-dimensional number line to the two-dimensional complex plane by using the horizontal axis for the real part and the vertical axis for the imaginary part. The complex number a + bi can be identified with the point (ab) Fig.1 An illustration of the complex plane

Basic Calculus:    .   3. Multiplication and Division  Euler's formula  Fig.2 Euler's formula for a general angle

Example 1:

Prove Proof:     Meanwhile, we know that  Example 2:

Prove and Proof:    Therefore, and .

Exercise: and Maclaurin series maxima code: taylor(1/(1-x),x,0,5); maxima code: taylor(log(1+x),x,0,5);  Hint: or  Hint: or 