There are nsolutions as there should be since we are finding the roots of a degree npolynomial in the algebraically closed Section The Complex PlaneThe equation jz ij=does not have any solution because jzjis a distance from the point zto the origin. Give an example to show that, in general, Arg(z1z2) 6= Arg(z1) +Arg(z2) (c.f. And clearly a distance is always non-negativeLet z= x+ iyand we have jz 1jjx+ iy 1jj(x 1) + iyj(Squaring both sides) (x 1)2 + y Exercise Let w=be a complex number such that
There are nsolutions as there should be since we are finding the roots of a degree npolynomial in the algebraically closed Section The Complex PlaneThe equation jz ij=does not have any solution because jzjis a distance from the point zto the origin. Give an example to show that, in general, Arg(z1z2) 6= Arg(z1) +Arg(z2) (c.f. And clearly a distance is always non-negativeLet z= x+ iyand we have jz 1jjx+ iy 1jj(x 1) + iyj(Squaring both sides) (x 1)2 + y Exercise Let w=be a complex number such that
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