Let $a$, $b$, $c$, and $d$ be four complex numbers on the unit circle, such that the line joining $a$ and $b$ is perpendicular to the line joining $c$ and $d$. Find a simple expression for $d$ in terms of $a$, $b$, and $c$.

47: 4 aisha changed 1.45 + 2.38 to 1.5 + 2.4 in order to estimate the sum. what estimation method did she use?

Mrs. robinson bought a novel at a bookstore on sale for 20% off its regular price of $29.99. mr chang bought the same novel at a different bookstore for 10% off its regular price of $25. which person received the better discount?

Adolphin jumps from 5 feet below the surface of the sea. jane wrote -5 to represent the death from which the dolphin jumped. what does zero represent in this situation?