Question 617526: Explain how complex numbers combine under the following operations:
Use one supporting example for each operation.
Include both algebraic and graphical interpretations in your responses.
Note: The graphical interpretation should demonstrate how to add and divide complex numbers solely using the graph of each complex number (not based upon the algebraic computation).
This is what I have so far To accompany the addition, I have it graphed out showing the parallelogram and that the diagnol is the sum of the vectors
what can i do to show how the division works graphically
if this would be easier to demonstrate with other numbers, work from scratch, change the numbers
When adding complex numbers, the real parts and the imaginary parts can not be combined. You can only add the real parts together, and the complex parts together, but they can not be added to each other. This means (5+2i)+(3+7i)= (8+9i). The 5 and 3 are combined, and the 2i and the 9i are combined.
When you divide, (6+3i)/(2-i),the first thing that you want to do is eliminate the complex number from the denominator. In order to do that, without changing the value of the fraction, you need to multiply by something that has a value of one, in this case the complex conjugate of the denominator or (2+i).
So, youre going to do ((6+3i)/(2-i))*((2+i)/(2+i)). The numerator, after multiplying out using foil, becomes (12+6i+6i+3(i^2)), the denominator, after using foil becomes (4+2i-2i-i). After simplifying, your fraction becomes (12+12i+3(i^2))/(4-i).
Answer by lynnlo(4155) (Show Source):