Answer:
BRO, u dont need to be a god :D, This is simple math and you just need to use your brains
Step-by-step explanation:
Given is a polynomial, and the values of the variables in it are given by showing what set are they an element of, right? It just gets easier from here
They tell us that 'z' is an element of set C, which stands for Complex Numbers.
And they also tell us that 'a' is an element of set Z, which stands for Integers, which are just numbers with a sign :).
They have also given us a root (solution) to the polynomial, which is also a complex number.
The two statements given are just there for us to verify that we are on the right track to the solution.
We can see that (z = 3 + i) which of course is a complex number, due to the presence of 'i', and 'a' is an integer for when we find its value.
Put it all together and we will get the answer.
Like this,
take the given value of 'z' and place it into the polynomial given, now keep your eyes open here. They said the value of z is as such when the polynomial is an equation which equals 0, so hence we get this:
P(z) = a(3+i)³ - 37(3+i)² + 66(3+i) - 10 = 0,
now just go on simplifying,
=> a(3³+i³+3×3²i+3×3i²) - 37(3²+2×3×i+i²) + 66×3 + 66×i - 10 = 0
=> a(27-i+27i-9i) - 37(9+6i-1) + 198 + 66i - 10 = 0
=> a(27+17i) - 37(8+6i) + 188 + 66i = 0
=> a(27+17i) = 296 + 222i - 188 - 66i
=> a(27+17i) = 108 + 156i
=> a = (108+156i) / (27+17i)
=> a = (108+156i)(27-17i) / (27)² - (17i)²
=> a = (5568 + 2376i) / (699 + 289)
=> a = 5568 + 2376i / 1488
DONNEEE....yayyyy....lol
