Presentation on theme: "An introduction to the complex number system. Through your time here at COCC, youve existed solely in the real number system, often represented by a number."— Presentation transcript:
The horizontal axis is still real.... Real axis
But...what to call the vertical axis? Real axis
Remember, in MTH 065, whenever you found the square root of a negative number....and just stopped? What did you write for your solution? No Real Number
Well, the region above and below the real axis is where all of those square roots of negative numbers live. This axis is called the imaginary axis...unfortunately. But why, Sean? Why is it called imaginary? Please tell us!
The imaginary unit is cleverly called i and is defined like this:
Real axis Imaginary axis i is placed right here on our new plane......notice that i is not real, so it doesnt touch the real axis.
Now we have Squaring both sides, we must also have
Real axis Imaginary axis i 2 goes right here... i 2 is not imaginary... its real!