Algebra
Problems related to equations, functions, polynomials, etc.
Problems in this category
Solve for $x$ and $y$ in the equation $\frac{x}{1+i} - \frac{y}{2-i} = \frac{1-5i}{3-2i}$.
Complex NumbersSystems of EquationsLinear Equations
2025/5/10
We are given several complex number problems. (2a) Express $\frac{1}{z}$ in the form $a + ib$, where...
Complex NumbersComplex ConjugateNumber Systems
2025/5/10
We are given the equation $\frac{1}{x+iy} + \frac{1}{1+3i} = 1$, where $x$ and $y$ are real numbers,...
Complex NumbersEquation SolvingComplex Conjugate
2025/5/10
Isaac and Seth share $£3600$. Seth gets twice as much money as Isaac. We need to find out how much S...
Linear EquationsWord ProblemRatio and Proportion
2025/5/10
The problem is to simplify the complex fraction $\frac{1 + \sqrt{2}i}{\sqrt{3} - 2i}$.
Complex NumbersComplex FractionsSimplificationConjugate
2025/5/10
The problem asks us to solve four systems of linear equations using the substitution method. System ...
Linear EquationsSystems of EquationsSubstitution Method
2025/5/10
The problem requires us to add two complex numbers: $(4 + i\sqrt{3})$ and $(-6 - 2i\sqrt{3})$.
Complex NumbersAdditionImaginary Numbers
2025/5/10
The problem asks us to expand the expression $(x - y - 1)(x - y + 3)$.
Polynomial ExpansionAlgebraic Manipulation
2025/5/10
Expand the expression $(x - y - 2z)^2$.
Algebraic ExpansionPolynomialsTrinomial Square
2025/5/10
The problem asks to expand the expression $(x - 2y + 3z)^2$.
Algebraic ExpansionTrinomial ExpansionPolynomials
2025/5/10