/**
 * Represents a complex number `a + bi`.
 */
export declare class Complex {
    readonly real: number;
    readonly imag: number;
    /**
     * Magnitude of the complex number.
     */
    readonly r: number;
    /**
     * Angle of the complex number.
     */
    readonly theta: number;
    /**
     * Define a complex number `a + bi`.
     * @param real The real portion.
     * @param imag The imaginary portion.
     */
    constructor(real: number, imag: number);
    /**
     * Create a complex number from polar coordinates.
     * @param r The magnitude (radius).
     * @param theta The angle in radians.
     * @returns A complex number represented by `r * e^{i theta}`.
     */
    static fromPolar(r: number, theta: number): Complex;
    /**
     * Determine whether this complex number is equal to another.
     * @param other The other complex number to compare.
     * @param tolerance Optional tolerance for approximate equality.
     * @returns `true` when both real and imaginary components are equal within tolerance.
     */
    equals(other: Complex, tolerance?: number): boolean;
    /**
     * Add another complex number to this one.
     * @param other The complex number to add.
     * @returns The sum of the two complex numbers.
     */
    plus(other: Complex): Complex;
    /**
     * Subtract another complex number from this one.
     * @param other The complex number to subtract.
     * @returns The difference of the two complex numbers.
     */
    minus(other: Complex): Complex;
    /**
     * Multiply this complex number by another.
     * @param other The complex number to multiply with.
     * @returns The product of the two complex numbers.
     */
    times(other: Complex): Complex;
    /**
     * Divide this complex number by another.
     * @param other The complex number to divide by.
     * @returns The quotient of the two complex numbers.
     */
    over(other: Complex): Complex;
    /**
     * Raise this complex number to a power.
     * @param exp The exponent.
     * @returns The complex number raised to the given power.
     */
    pow(exp: number): Complex;
}