1310, 2.4
Complex numbers
Solve
0144x
2
Now, solve
04x
2
Big problems! There is no solution in the Real numbers…so we’ll come up with a new
number system: Complex numbers!
The basic building block is
1
. This new number is also called “i”…it used to be
considered “imaginary” but it’s really not…it’s a basic fact of everyday life as in the
equations that govern electric power generation.
This new number , “i”, comes up as part of the solution to equation
04x
2
.
It turns out that it’s not a new number system, it’s an expansion of the real numbers into a
system called the complex numbers. A complex number is a number of the form
a + bi where the “i” is
1
.
So that old familiar number 2 is 2 + 0i , 3 is 3 + 0i, and 0.5 is complex with zero times i,
too. In fact, every real number has b = 0 in it’s complex form.
1
is 0 + 1i.
There are two parts to a complex number the “a” called the real part and the “b” called
the complex part.
1
