SOLUTION: Explain how complex numbers combine under the following operations: a. Addition b. Division The graphical interpretation should demonstrate how to add and divide complex nu

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Question 564049: Explain how complex numbers combine under the following operations:
a. Addition
b. Division

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).
*** I understand the concept of ;
The standard form of complex number is ;
(a + bi) + (a + bi)
(a + a) +(bi +bi)
2a + 2bi
Or … (3 + 2i) + (1+i)
(3+1) + (2i + i) = 4 + 3i

So WHAT IS THE GRAPHICAL INTERPRETATION; demonstrate how to add and divide complex numbers solely using the graph of each complex number
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
Adding complex numbers is quite simple to show graphically, since complex numbers add just like vectors (add the individual components). The sum of the complex numbers is simply the resultant vector formed by the other numbers.

Multiplying/dividing is a little more difficult to show graphically. Perhaps you could represent two complex numbers z1, z2 by



(note that Euler's formula states that e^(ix) = cos x + i sin x, so you can represent any complex number in the above form).

Then,



Graphically, this means that the radius is numerically equal to the product of the radii of r1 and r2, and the angle formed by z1z2 is equal to the sum of the angles formed by z1 and z2. Representing division graphically is similar; think of division as multiplying by 1 over the complex number. Or, find some way to "undo" the multiplication.