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```
use std::ops;
use std::cmp;

pub struct Polar {
pub r: f64,
pub theta: f64,
}

impl Polar {
pub fn to_complex(self) -> Complex {
Complex {
real: self.r * self.theta.cos(),
img: self.r * self.theta.sin(),
}
}
}

#[derive(Copy, Clone, Debug, Default)]
pub struct Complex {
pub real: f64,
pub img: f64,
}

impl Complex {
pub fn new(real : f64, img: f64) -> Complex{
Complex {
real: real,
img: img
}
}

pub fn i() -> Complex {
Complex {
real: 0.0,
img: 1.0,
}
}

pub fn to_polar(&self) -> Polar {
let r2 = self.modulus();
let polar = Polar {
r : (r2).sqrt(),
theta : (self.real/self.img).atan(),
};
polar
}

pub fn conjugate(&self) -> Complex {
Complex {
real: self.real,
img: -self.img
}
}

pub fn exp(&self) -> Complex {
let pol = self.to_polar();
let exp_r = pol.r.exp();
Complex{
real: exp_r * pol.theta.cos(),
img:  exp_r * pol.theta.sin(),
}
}

pub fn modulus(&self) -> f64 {
self.real * self.real + self.img * self.img
}

pub fn cos(&self) -> Complex {
Complex {
real: (self.real).cos()*(self.img).cosh(),
img: -(self.real).sin()*(self.img).sinh(),
}
}

pub fn sin(&self) -> Complex {
Complex {
real: (self.real).sin()*(self.img).cosh(),
img: -(self.real).cos()*(self.img).sinh(),
}
}
}

impl ops::Neg for Complex {
type Output = Complex;

fn neg(self) -> Complex {
//TODO: divide by two
Complex { real: - self.real, img: -self.img}
}
}

impl ops::Add< Complex> for Complex {
type Output = Complex;

fn add(self, other:  Complex) -> Complex {
Complex {
real: self.real + other.real,
img: self.img + other.img
}
}
}

impl cmp::PartialEq for Complex {
fn eq(&self, other: &Complex) -> bool {
((self.real == other.real) & (self.img == other.img))
}
}

impl ops::Sub< Complex> for Complex {
type Output = Complex;

fn sub(self, other:  Complex) -> Complex {
self + (-other)
}
}

impl ops::Mul<Complex> for Complex {
type Output = Complex;

fn mul(self, other: Complex) -> Complex {
Complex {
real: self.real*other.real - self.img*other.img,
img: self.img * other.real + self.real * other.img
}
}
}

impl ops::Mul<f64> for  Complex {
type Output = Complex;

fn mul(self, other: f64) -> Complex {
Complex {
real: self.real*other,
img: self.img* other,
}
}
}

impl ops::Div<f64> for  Complex {
type Output = Complex;

fn div(self, other: f64) -> Complex {
Complex {
real: self.real/other,
img: self.img/other,
}
}
}

impl ops::Div< Complex> for  Complex {
type Output = Complex;

fn div(self, other:  Complex) -> Complex {
let den = other.real * other.real + other.img * other.img;
let x = (self.real*other.real + self.img*other.img)/den;
let y = (self.img * other.real - self.real * other.img)/den;

Complex {
real: x,
img: y,
}
}
}

```