Complex Numbers/Introduction

Notice: Incomplete

Prerequisites edit

All four operations (+, -, *, /) for the real numbers

The purpose of parentheses in math

Box method for multiplication and/or FOIL

Meaning of Complex Numbers edit

What does i mean? edit

i is a 'fake', or imaginary number such that i*i=-1. We need to make up a number because 1*1=1 and -1*-1=1.

Complex numbers edit

Complex numbers are numbers that 'look like' all of the following:





Math of Complex Numbers edit

Add edit

To add complex numbers, you add similar things, so (1+2i)+(3+4i)=(1+3)+(2+4)i=4+6i

Take away edit

To 'take away' complex numbers, you 'take away' similar things, so (1+2i)-(3+4i)=(1-3)+(2-4)i=-2-2i

Times edit

To 'multiply' complex numbers, you 'multiply' similar things, so (1+2i)(3+4i)=(1)(3)+(1)(4i)+(2i)(3)+(2i)(4i)

With Box Method edit

Using the example of (1+2i)*(3+4i), we get:

1 2i
3 1*3=3 2i*3=6i
4i 1*4i=4i 2i*4i=8i*i=-8

Going across both diagonals, we get:


With FOIL edit

To multiply complex numbers, you multiply using FOIL, like this: (1+2i)*(3+4i)=(1*3)+(1*4i)+(2i*3)+(2i*4i)=3+4i+6i-8=-5+10i

Divide edit

To divide complex numbers, you turn it into a multiplication problem, like this:  , which can be solved normally. This works because  

  and dividing is just multiplication by the reciprocal.

3 4i

Conjugate edit

The conjugate of a complex number is the number you get if you replace the + linking the real and imaginary parts with - or vice versa. Some examples include:

Complex number Conjugate
1+2i 1-2i
1-2i 1+2i
-1+2i -1-2i
-1-2i -1+2i

The Complex Plane edit