Question

T've got a mental block with this one - my cousin's homework. The first part is easy but i'm not sure how to proceed with the second.
Verify that x = 2 and y = -1 satisfy the system of equations
x^3 - 3xy^2 = 2, 3x^2y - y^3 = -11.

Hence find the cube root of 2 - 11i.

Answer 1

Its probably obvious but just can't get my head around it somehow..

Answer 2

Well yeah it is quite easy:
2-11i = x^3 -3xy^2 + 3x^2y - y^3 = (x-y)^3

Answer 3

if x=2 and y=-1 satisfy the system; then they will both be true for the stated values

Answer 4

i spose this is the 'second' part: Hence find the cube root of 2 - 11i.

Answer 5

i know if i let
(x + yi)^3 = 2 - 11i

then plug in x = 2 and y = -1 into the above then LHS = RHS but how can i justify that?

Answer 6

It's already justified by part A.

Answer 7

so cube root = 2 - i

Answer 8

Yep !

Answer 9

yes

Answer 10

not difficult!

Answer 11

lol

Answer 12

Indeed :P