B. Simplifying "i" Raised to Some Number
- Imaginary unit "i" is equal to
- Complex number in standard form is a + bi.
- "a" and "b" are real numbers.
- Pure imaginary number is in the form bi.
C. Simplifying the Square Root of a Negative Number
- Divide the exponent by 4 and determine the remainder
- Raise "i" to that power to simplify.
- i = i
- i2 = -1
- i3 = -i
- i4 = 1
D. Graphing a Complex Number in Standard Form a + bi
- Factor out the square root of -1, which equals "i".
- Simplify the radical of the positive number if possible.
E. Operations with Complex Numbers
- Rename the axes
Start at the origin.
Use the values of "a" and "b" to graph the point.
- The traditional x-axis is the real axis or "a".
- The traditional y-axis is the imaginary axis or "b".
Graph the point after making these two moves.
- The value of "a" determines whether to move left or right along the real axis.
- The value of "b" determines whether to move up or down along the imaginary axis.
- Perform the operations as though "i" were any variable.
- Simplify "i" when possible. Refer to Part B above.
- Write answers in standard form a + bi.