SOMEONE PLEASE HELP! IVE BEEN ASKING FOR DAYS AND ITS DUE TODAY. Please provide a step by step explanation. Thank you.

The complex numbers $z$ and $w$ satisfy $|z| = |w| = 1$ and $zw \ne -1.$

(a) Prove that $\overline{z} = \frac{1}{z}$ and $\overline{w} = \frac{1}{w}.$

(b) Prove that $\frac{z + w}{zw + 1}$ is a real number.

Adolphin is swimming with her friend. the dolphin jumps to a height of 4.54.54, point, 5 meters above the surface of the water as her friend swims 9.89.89, point, 8 meters directly below her. what is the position of the dolphin's friend relative to the surface of the water? meters

Find the average rate of change for the given function drom x=1 to x=2

Linda and ralph have signed a contract to purchase a home. the closing date is april 27, and the buyer owns the property on the day of closing. the selling price of the home is $782,500. linda and ralph obtained a fixed-rate mortgage from a bank for $685,000 at 7.35% interest. the seller has already paid $14,578.15 in property taxes for the coming year. how much will linda and ralph owe in prorated expenses? (3 points) $64,925.65 $34,347.06 $10,496.82 $9,945.06