11.2. Arithmetic with Complex Numbers http://www.ck12.org
11.2 Arithmetic with Complex Numbers
Here you will add, subtract, multiply and divide complex numbers. You will also find the absolute value of complex
numbers and plot complex numbers in the complex plane.
The idea of a complex number can be hard to comprehend, especially when you start thinking about absolute value.
In the past you may have thought of the absolute value of a number as just the number itself or its positive version.
How should you think about the absolute value of a complex number?
Watch This
MEDIA
Click image to the left for use the URL below.
URL: http://www.ck12.org/flx/render/embeddedobject/62131http://www.youtube.com/watch?v=htiloYIILqs James Sousa: Complex Number Operations
Guidance
Complex numbers follow all the same rules as real numbers for the operations of adding, subtracting, multiplying
and dividing. There are a few important ideas to remember when working with complex numbers:
- When simplifying, you must remember to combine imaginary parts with imaginary parts and real parts with real
parts. For example, 4+ 5 i+ 2 − 3 i= 6 + 2 i. - If you end up with a complex number in the denominator of a fraction, eliminate it by multiplying both the
numerator and denominator by the complex conjugate of the denominator. - The powers ofiare:
- i=
√
− 1
- i^2 =− 1
- i^3 =−√− 1 =−i
- i^4 = 1
- i^5 =i
-... and the pattern repeats
The complex plane is set up in the same way as the regularx,yplane, except that real numbers are counted
horizontally and complex numbers are counted vertically. The following is the number 4+ 3 iplotted in the complex
number plane. Notice how the point is four units over and three units up.