Explain how complex numbers combine algebraically and graphically (solely using the graph, meaning just graphing the result of the algebraic computation is not sufficient) under the following operations:

a. Addition

b. Division

Addition has been covered in previos question.

For division follow the rule:

lets take 2 complex numbers x1+iy1

and x2+iy2

x1+iy1/x2+iy2

multiply by conjugate of denominator

so,(x1+iy1/x2+iy2)*(x2-iy2/x2-iy2)

=(x1x2-ix1y2+x2iy1+y1y2)/x2^2+y2^2

gives the division of the two complex number.

for graphing we have to use polar form

z1=r1e^i@1

z2=r2e^@2

dividing 2 polar number gives

z1/z2=r1/r2 e^i(@1-@2)

we have to plot new polar number by taking radius as r1/r2 and angle as (@1-@2)

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