Question

A circle has a diameter with endpoints at -2+I and -6-11i. What is the center of the circle

Answer 1

so  hmm, using those on the a+bi values on the x-axis and imaginary axis

$\bf \begin{cases} -2+1i\\ -6-11i \end{cases}\implies \begin{cases} -2,1\\ -6,-11 \end{cases}\\\\ -----------------------------\\\\ \textit{middle point of 2 points }\\ \quad \\ \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) &({{ -2}}\quad ,&{{ 1}})\quad % (c,d) &({{ -6}}\quad ,&{{ -11}}) \end{array}\qquad % coordinates of midpoint \left(\cfrac{{{ x_2}} + {{ x_1}}}{2}\quad ,\quad \cfrac{{{ y_2}} + {{ y_1}}}{2} \right) \\\\\\ \left(\cfrac{-2+(-2)}{2}\quad ,\quad \cfrac{-11+1}{2} \right)$

the middle point of the diameter chord, is of course, the center of the circle

Answer 2

Answer:

B.) -4 - 5i

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Here is how I found my answer !

-To find a midpoint between 2 complex numbers is to determine the average

1.) Add the two end points

(-2 + i) + (-6 - 11i)

2.) Divide it all by 2

(-2 + i) + (-6 - 11i) / 2

3.) Numerator should end up with -8 - 10i

-8 - 10i / 2

4.) Finish dividing

Answer is :  -4 - 5i

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Hope this gives a better understanding of how to solve it !! :D