- #1
jammed
- 26
- 0
Hey i have a question:
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.
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.