Asked by Aditya
The system of equations
|z - 2 - 2i| = \sqrt{23},
|z - 8 - 5i| = \sqrt{38}
has two solutions z1 and z2 in complex numbers. Find (z1 + z2)/2.
Im really just plain old confused. Could anyone help me out?
|z - 2 - 2i| = \sqrt{23},
|z - 8 - 5i| = \sqrt{38}
has two solutions z1 and z2 in complex numbers. Find (z1 + z2)/2.
Im really just plain old confused. Could anyone help me out?
Answers
Answered by
Steve
if z = x+yi, you have two equations:
(x-2)^2 + (y-2)^2 = 23
(x-8)^2 + (y-5)^2 = 38
They intersect at
(1/5(20±3√10), 3/5(5∓2√10))
check:
(1/5(20+3√10)-2)^2 + (3/5(5-2√10)-2)^2 = 23
You can verify the other.
(x-2)^2 + (y-2)^2 = 23
(x-8)^2 + (y-5)^2 = 38
They intersect at
(1/5(20±3√10), 3/5(5∓2√10))
check:
(1/5(20+3√10)-2)^2 + (3/5(5-2√10)-2)^2 = 23
You can verify the other.
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