Algebra
Problems related to equations, functions, polynomials, etc.
Problems in this category
Given two complex numbers $Z_a = 1 + \sqrt{3}i$ and $Z_b = 2 - 2i$, we are asked to: I. Convert $Z_a...
Complex NumbersPolar FormDe Moivre's TheoremComplex Number MultiplicationComplex Number DivisionRoots of Complex Numbers
2025/6/27
The problem involves complex numbers. Given $z_1 = 5 + 2i$, $z_2 = 7 + yi$, and $z_3 = x - 4i$, we n...
Complex NumbersComplex Number ArithmeticComplex ConjugateSquare Root of Complex Number
2025/6/27
The problem asks us to find the range of values for the constant $a$ such that the equation $4^x - a...
Quadratic EquationsInequalitiesExponentsRoots of EquationsDiscriminant
2025/6/27
Given $A = \{1, 2\}$ and $B = \mathbb{R}$, we need to sketch the graph of $R = A \times B$. We need ...
SetsRelationsFunctionsCartesian ProductGraphs
2025/6/27
Solve the equation $ \lceil x^2 - x \rceil = x + 3 $ for $x \in \mathbb{R}$, where $ \lceil x \rceil...
Ceiling FunctionQuadratic EquationsInteger Solutions
2025/6/27
A lemming runs from point A to a cliff at B at 4 m/s, jumps over the edge and falls to point C at an...
Word ProblemLinear EquationsDistance, Speed, and Time
2025/6/27
Given three matrices $X$, $Y$, and $Z$ as follows: $X = \begin{bmatrix} 5 & 4 & -7 \\ -3 & p & 5 \en...
MatricesMatrix TransposeMatrix MultiplicationMatrix Addition
2025/6/27
We have two problems to solve. Problem 6: A man is 32 years older than his son. Ten years ago, the m...
Word ProblemsSystems of EquationsLinear EquationsRate ProblemsDistance, Rate, and Time
2025/6/26
We are given two systems of equations to solve. System 1: $3m - n = 5$ $2m + 5n = 7$ System 2: $5c -...
Systems of EquationsLinear EquationsSubstitution
2025/6/26
We are given 8 problems. Let's solve them one by one. Problem 1: A man receives a total of $17800$ o...
Linear EquationsWord ProblemsRatio and ProportionGeometryQuadratic EquationsDistance, Rate, and Time
2025/6/26