problem archive
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If (a + ib)(c + id)(e + if)(g + ih) = A + iB, then show that (a^2 + b^2)(c^2 + d^2)(e^2 + f^2)(g^2 + h^2) = A^2 + B^2. -
If \left(\frac{1 + i}{1 - i}\right)^m = 1, then find the least positive integral value of m. -
Let $z_1 = a + ib$ and $z_2 = c + id$. Then (i) $z_1 + z_2 = (a + c) + i (b + d)$ (ii) $z_1 z_2 = (ac - bd) + i (ad + bc)$ -
A father is three times as old as his son... -
You have a 5-liter jug and a 3-liter jug... -
Three friends check into a hotel room that costs $30... -
A farmer has a certain number of sheep and cows... -
Two trains leave a station at the same time... -
You have a bag of coins: some are gold and some are silver... -
A chessboard is an 8x8 grid... -
A train leaves a tunnel at a speed of 60 miles per hour... -
In a room of 23 people, what is the probability... -
You have two hourglasses: one measures 7 minutes... -
You are given 9 balls, all of the same size... -
You are driving a bus. At the first stop... -
In a school, 100 students were surveyed on their preference between soccer, basketball, and tennis... -
If it takes 5 machines 5 minutes to make 5 widgets... -
A man spends exactly $10 to buy 100 animals... -
A man is on a diet and buys a 100-pound watermelon... -
There are three boxes: one with apples, one with oranges...