2.4 - Complex Numbers

Chapter 2. 4 Complex Numbers

There are real numbers: any positive or negative number including integers, rational, and irrational numbers
   ex: 5, 7.9, 323

And there are imaginary numbers: a number that when squared gives a negative result

Because we can't find the square root of -1, we use i in it's place.

This would make these examples...

Then there are complex numbers: which are made up of both real and imaginary numbers

They take the form of a + bi which is also called standard form.

 

Addition of Complex Numbers

(a + bi) + (c + di) = (a + c) + (b + d)i

ex: (13 + 5i) + (2 + 26i)

      (13 + 2) + (5 + 26)i

      15 + 31i

Subtraction of Complex Numbers

(a + bi) - (c + di) = (a - c) + (b - d)i

ex: (4 - i) - (7 + 3i)

      (4 - 7) + (-i - 3i)

      -3 - 4i

Multiplication of Complex Numbers

You can use foil with multiplication.

Dividing Complex Numbers

To find the quotient of a + bi and c + di where c and d are both not zero, multiply the numerator and denominator by the conjugate of the denominator.

Graphing Complex Numbers

When graphing complex numbers, the coordinate system is called the complex plane. The horizontal plane is called the real axis, and the vertical axis is the imaginary axis. 

Exponents

The pattern repeats from i to i to the fourth so say you are given 

And you don't know whether it is i, -1, -i, or 1, y

ou can divide the exponent by 4 and the remainder tells you which it is

The remainder is 2, so you know that 

That's about it, yep... cool... yay math.

Carly