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Complex Arithmetic
Once you probably thought the real numbers were all that there
were.
But when you learned that $\sqrt{-1}$
was another type of number, then everything changed. Most of the
time,
elementary math courses just introduce imaginary numbers, but don't let
you get
your hands dirty with them. Instead, you are supposed to wait
until a
complex variables course in either upper level college or graduate
school.
But if you know some trigonometry, we introduce the mechanics of the
situation
here! Check out these pages ...
- Imaginary Numbers:
understanding what we mean when we say that $\sqrt{-1}$ is an imaginary,
or complex, number
- Square Root of i:
the square root of a complex number is still a complex number
- Square Roots of Imaginary Numbers,
Using Algebra: how to find them, sometimes, but its messy
- Square
Root Calculator: gives square roots of complex numbers in
radical form
- Imaginary Numbers and Trigonometry:
an
easier
approach
to
finding square roots, and all kinds of powers, of complex numbers
- Using i as an Exponent:
a
power
series
result
from calculus allows us to recognize that complex exponents are related to trigonometric functions
- Functions of Complex Numbers:
how
to
do
logarithmic,
trigonometric, and hyperbolic functions of complex numbers, and their inverses.
- Summary of Complex Number Operations:
a table of formulas
Once functions are defined for complex numbers, it becomes possible
to study the functions, not just compute values with the
functions. Here are some pages to explore the functions...