The complex numbers are
all the numbers that you
get by putting together
real numbers and the square
root of -1, which is called
i. Anything you can get
by adding, subtracting,
multiplying, and dividing
real numbers and i is
called a complex number.
As it turns out, this
means that they are anything
of the form a+bi, where
a and b are real numbers.
This article is about
how to do the four basic
arithmetic operations,
adding, subtracting, multiplying,
and dividing with complex
numbers. To master this
arithmetic all you really
need to know is that i
is the square root of
-1 and that anything you
normally do in algebra
with variables, you can
do with i.
Addition
To add complex numbers,
just treat the i like a
variable and combine like
terms.
Example:
(3+2i)+(1-5i)=3+2i+1-5i=4-3i
Subtraction
To subtract to the same
thing, but just like with
variables you have to make
sure to change the signs
of both terms in the second
one.
Example:
(5-i)-(3-2i)=5-i-3+2i=2+i
Multiplication
Here just like with variables,
we use FOIL, but one different
thing happens, we will get
an i squared, which we have
to turn into -1 because
i is the square root of
-1.
Example:
(4+3i)(3-2i)=12-8i+9i-6i
2=12-8i+9i+6=18+i
Division
Division is just a little
bit harder. To get it into
its standard form of a+bi
we need to do something
sort of like rationalizing
the denominator. We need
to multiply top and bottom
by what is called the complex
conjugate. The complex conjugate
is what you get if you change
the sign of the imaginary
part, but keep the real
part as is.
Example:
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Now you know all about
complex number arithmetic.
