Try it on paper first. A hint, the key idea and the worked solution are here when you need them.
The points , and are three corners , and of a parallelogram , in that order. Find the fourth corner and its distance from the origin.
On the Argand plane, is the point . The modulus is the distance from the origin, and is the mirror image in the real axis. The distance between and is , and their midpoint is .
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Step 1. Equal midpoints. The diagonals and have the same midpoint, so .
Step 2. Solve for D. .
Step 3. The distance. .
Answer: , at distance from the origin.
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