maths.free › Precalculus › Complex numbers

Complex numbers

i² = −1, arithmetic in the complex plane, modulus and conjugates.

Allowing one new number, i with i² = −1, makes every polynomial equation solvable. Complex numbers add like vectors and multiply by multiplying lengths and adding angles; the modulus |a + bi| = √(a² + b²) is the distance from 0. The solver evaluates the arithmetic exactly and the quadratic pages show where complex roots come from.

Ишлатилган мисол: (1 + 2i)*(3 - i)

Arithmetic · Arithmetic

Evaluate (1 + 2I)·(3 - I)

\left(1 + 2 i\right) \left(3 - i\right)

Қадамма-қадам

  1. \left(1 + 2 i\right) \left(3 - i\right) = 5 + 5 i

    Evaluate.

Жавобни кўрсатиш
5 + 5 i

Ўзингизни синаб кўринг

Кўпроқ Precalculus

Polynomial functionsRational functionsSequences and seriesThe binomial theoremConic sectionsVectors