Complex Arithmetic

Once you probably thought the real numbers were all that there were.  But when you learned that 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 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...

• The Complex Polynomial Function (Standard Form)
• The Complex Polynomial Function (Factored Form)
• The Complex Exponential Function
• The Complex Logarithmic Function
• The Complex Sine Function
• The Complex Arcsine Function
• The Complex Function