Hello, williamb!
From the given points, we have:Find a complex polynomial which has the points:
Write your answers in the form
. .
From [2]: .
And we have: .
From [4], we have: .
Therefore, the function is: .
QUESTION: Find a (complex) quadratic polynomial P(z)=a+bz+cz2 which interpolates the data: (-1,i),(0,i), (6 i, 0)
Write your answers a ,b, c in form x + iy
My Work:
So I have three different equations, using my x coordinate for my z values and my y coordinate as my P(z) values.
Equations:
i = a - b + c
i = a
0 = a + 6ib
I (tried) to solve each value by matrix reduction
__1_-1__1__i
__1_0__0 __i
__1_6i_-36_0
__1__-1___ 1____i
__0__ 1__(-6/i) _(-i/6)
__0__-1____1___0
(i continue to solve it until i get...):
a=i
b+(6i)c = -1/6
(1+6i)c = -1/6
if this IS right, i don't know how to actually solve the system
i end up getting b=c,
but if they answer has to be in x+iy how do i put it in this form??
thanks for the help!