1. ## Quadratic and other polynomials

Please note: two complex numbers are equal when their real parts are equal and their imaginary parts are equal.
i.e., if a+bi=c+di, then a=c and b=d

Find real numbers X and Y for which:

(X+yi)(y-i)=-4-7i

2. Originally Posted by Tessarina
Please note: two complex numbers are equal when their real parts are equal and their imaginary parts are equal.
i.e., if a+bi=c+di, then a=c and b=d

Find real numbers X and Y for which:

(X+yi)(y-i)=-4-7i

$\displaystyle (x + yi)(y - i) = xy - xi + y^2i -i^2y$

$\displaystyle xy + (y^2 - x)i + y$

$\displaystyle y(x + 1) + (y^2 - x)i$.

The real parts need to be equal, and the imaginary parts need to be equal.

So $\displaystyle y(x + 1) = -4$ and $\displaystyle y^2 - x = -7$.

Solve these equations simultaneously for $\displaystyle x$ and $\displaystyle y$.

3. Originally Posted by Tessarina
Please note: two complex numbers are equal when their real parts are equal and their imaginary parts are equal.
i.e., if a+bi=c+di, then a=c and b=d

Find real numbers X and Y for which:

(X+yi)(y-i)=-4-7i
Thanks for helping, but i tried to work it out and i still cant get it,

This is the answer in the back of the book---
X=-1
Y=0

4. Either you have copied the problem incorrectly or the answer is given incorrectly. If x= -1 and y= 0 then (x+yi)(y-i)= (-1+0i)(0- i)= (-1)(-i)= i, not -4- 7i.