Distance Of A Point From A Plane

Step 1: Use the condition that is the midpoint of and .
The midpoint formula for complex numbers is: Substitute the values of and : So, .
Step 2: Substitute into the given equation .
Substitute , , and into the equation: This simplifies to: Expanding the terms: Combine real and imaginary parts:
Step 3: Solve for and .
For the equation to be true, both the real and imaginary parts must be zero. This gives us the system of equations:
Step 4: Solve the system of equations.
From the second equation, solve for : Substitute this into the first equation: Simplify: Now substitute into :
Step 5: Calculate . Thus, the value of is .