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Q. One root of the cubic equation is z^3 + az + 10 = 0 is 1 + 2i.

(i). Find the value of the real constant a.

(ii). Show all the roots of the equation on an Argand Diagram.

(iii). Show that all three roots satisfy the equation |6z - 1| = 13, and show the locus represented by this equation on your diagram.

I did (i) and (ii) second part easily. The only problem I am facing is that of locus. I mean if the last part was like |z - 1| = 13, I know that the locus is a circle of radius 13 with center (1,0) but here it is different. I mean does 6z affect the locus. If it does then what should be the locus and if it doesnot what is the reason behind it.

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# Complex Number - Locus

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