Complex Number System/Complex Plane problem. I know that the correct answer is C, but I don't understand how to arrive at that answer. See attached.

Question

Complex Number System/Complex Plane problem.  I know that the correct answer is C, but I don't understand how to arrive at that answer.  See attached.

anonymous · Answer

attachment

anonymous · Answer

lord is this problem ever designed to confuse!  the idea is that the equation for the circle is 
$$x^2+y^2=1$$ and the line is 
$$y=x+2$$

anonymous · Answer

so you can rewrite the first equation as 
$$x^2+(x+2)^2=1$$ and solve for x

anonymous · Answer

substitute the line equation into y of the equation of the circle?

anonymous · Answer

$$x^2+x^2+4x+4=1$$
$$2x^2+4x+3=0$$

anonymous · Answer

then the quadratic formula will give you two complex solutions

anonymous · Answer

ahhhh, that's where the complex numbers are coming into play.

anonymous · Answer

okay, I can do that....just like when finding the roots of characteristic polynomials.

anonymous · Answer

yes, but more basically it is just like solving a quadratic equation

anonymous · Answer

right

anonymous · Answer

Thank you so much!!

anonymous · Answer

$$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$$

anonymous · Answer

yw

anonymous · Answer

btw  you get choice c  i believe

anonymous · Answer

I have the answer key,, it is C...yes

anonymous · Answer

thanks again

jamesj · Answer

@sat73: agreed; terrible question