Doug C. answered • 07/30/22
Math Tutor with Reputation to make difficult concepts understandable
Here is one way to do it.
Opposite sides of a parallelogram are parallel and also equal.
Find the distance from A to B. Then OC must have that same distance.
Find the slope of line through A and B. Then the line through O and C must have the same slope.
Consider the circle with center at O and radius distance from A to B along the line through O with same slope as AB. The points of intersection of those graphs will be give the a,b values for C = a+bi.
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Doug C.
Well there is a different way to think about it, but it is essentially performing the same tasks. The distance from A to B is 5 (distance formula). The slope of the line through A and B is -4/3 (slope formula). The equation of the line through O and C is y = (-4/3)x (parallel lines have the same slope and the y-intercept is 0). This means the coordinates of point C will be (x , (-4/3)x). The distance from O to C must be 5, so sqrt(x^2+((-4/3)x)^2) = 5. Therefore x^2 + 16/9 x^2 = 25. Solve for x to get either -3 or 3. Since you are looking for parallelogram OABC, choose x = 3, which gives y = -4.08/03/22
Doug C.
Which means the complex number associated with C is 3-4i.08/03/22
Mike I.
that sounds complicated isnt there another way to do it??08/03/22