Complex Number Equations: Solving for z and Finding the Perpendicular Bisector

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To solve the equation z + 2i z̅ = -9 + 2i, substitute z = x + iy and its conjugate z̅ = x - iy, then equate real and imaginary parts to form two equations. For the perpendicular bisector described by |z - 9 + 9i| = |z - 6 + 3i|, express both sides in terms of x and y, leading to the equations √((x - 9)² + (y + 9)²) = √((x - 6)² + (y - 3)²). Squaring both sides eliminates the square roots, allowing for simplification and solving for x and y. This process ultimately leads to determining the slope (m) and y-intercept (c) of the line. Understanding these steps is crucial for accurately solving complex number equations.
  • #31
Here are my 3 Questions so far:
Q1 and Q3 on the images represent the 2 I asked in the OP. The Q2 is one I have done myself and I believe to be right. Is this any better?
 

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  • #32
King_Silver said:
Here are my 3 Questions so far:
Q1 and Q3 on the images represent the 2 I asked in the OP. The Q2 is one I have done myself and I believe to be right. Is this any better?

any help? :)
 

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