/**
 * @file      Complex.ts
 * @author    Gage Sorrell <gage@sorrell.sh>
 * @copyright (c) 2026 Gage Sorrell
 * @license   MIT
 */
import { Operator } from "tsover-runtime";
/**
 * Elements of the complex plane, $\mathbf{C} = \mathbf{R}[x] / [ x^2 + 1 ]$.
 */
export declare class FComplex {
    readonly Re: number;
    readonly Im: number;
    static Zero: FComplex;
    /**
     * The copy constructor for {@link FComplex} numbers.
     *
     * @param Z - The existing {@link FComplex} number to copy.
     *
     * @example
     * ```typescript
     * const Z: FComplex = 3 + 2 * i;
     * const W: FComplex = new FComplex(Z);
     * // `W.Re === Z.Re` <- `true`
     * // `W.Im === Z.Im` <- `true`
     * ```
     */
    constructor(Z: FComplex);
    /**
     * Construct an {@link FComplex} number by specifying the real
     * and imaginary components.
     *
     * @param A - The real component of the {@link FComplex} number.
     * @param B - The imaginary component of the {@link FComplex} number.
     *
     * @example
     * ```typescript
     * const Theta: number = 0.5;
     * const OnUnitDisk: FComplex = new FComplex(Math.sin(Theta), Math.cos(Theta));
     * ```
     */
    constructor(A: number, B: number);
    /**
     * Get the modulus of this {@link FComplex} number.
     *
     * @returns {number} The modulus of this {@link FComplex} number.
     */
    get Mod(): number;
    /**
     * Get the modulus of this {@link FComplex} number.
     *
     * @returns {number} The modulus of this {@link FComplex} number.
     */
    get Theta(): number;
    [Operator.star](A: FComplex, B: FComplex): FComplex;
    [Operator.star](A: FComplex, B: number): FComplex;
    [Operator.star](A: number, B: FComplex): FComplex;
    [Operator.plus](A: FComplex, B: FComplex): FComplex;
    [Operator.plus](A: FComplex, B: number): FComplex;
    [Operator.plus](A: number, B: FComplex): FComplex;
}
export declare const i: FComplex;
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