import { Complex as ComplexClass } from 'complex.js';
/**
 * JSON representation of a Complex number
 */
export interface ComplexJSON {
    mathjs: 'Complex';
    re: number;
    im: number;
}
/**
 * Polar representation of a Complex number
 */
export interface PolarCoordinates {
    r: number;
    phi: number;
}
/**
 * Formatting options for Complex numbers
 */
export interface ComplexFormatOptions {
    precision?: number;
    notation?: 'auto' | 'fixed' | 'exponential' | 'engineering';
    lowerExp?: number;
    upperExp?: number;
    wordSize?: number;
}
/**
 * Extended Complex type with mathjs additions
 */
export interface Complex extends ComplexClass {
    type: 'Complex';
    isComplex: true;
    toJSON(): ComplexJSON;
    toPolar(): PolarCoordinates;
    format(options?: number | ComplexFormatOptions | ((value: number) => string)): string;
}
/**
 * Input for creating a Complex from polar coordinates
 */
export interface PolarInput {
    r: number;
    phi: number;
}
/**
 * Input for creating a Complex from absolute value and argument
 */
export interface AbsArgInput {
    abs: number;
    arg: number;
}
/**
 * Complex constructor interface with static methods
 */
export interface ComplexConstructor {
    new (a?: number | string | ComplexJSON | PolarInput | AbsArgInput, b?: number): Complex;
    (a?: number | string | ComplexJSON | PolarInput | AbsArgInput, b?: number): Complex;
    prototype: Complex;
    fromPolar: {
        (polar: PolarInput): Complex;
        (r: number, phi: number): Complex;
    };
    fromJSON: (json: ComplexJSON) => Complex;
    compare: (a: Complex, b: Complex) => number;
    ZERO: Complex;
    ONE: Complex;
    I: Complex;
    PI: Complex;
    E: Complex;
    INFINITY: Complex;
    NAN: Complex;
    EPSILON: number;
}
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