From ae1af2e2a82c30a336a0de8c264b904f64ab2e59 Mon Sep 17 00:00:00 2001
From: Jidong Xiao <xiaoj8@rpi.edu>
Date: Sun, 15 Oct 2023 21:10:03 -0400
Subject: [PATCH] adjusting format

---
 lectures/14_operators/README.md | 72 +++++++++++++++------------------
 1 file changed, 33 insertions(+), 39 deletions(-)

diff --git a/lectures/14_operators/README.md b/lectures/14_operators/README.md
index c186124..c8707b5 100644
--- a/lectures/14_operators/README.md
+++ b/lectures/14_operators/README.md
@@ -4,37 +4,31 @@
 
 ## 14.1 Complex Numbers — A Brief Review
 
-- Complex numbers take the form z = a + bi, where i =
-√
-−1 and a and b are real. a is called the real part, b is
-called the imaginary part.
-- If w = c + di, then
-– w + z = (a + c) + (b + d)i,
-– w − z = (a − c) + (b − d)i, and
-– w × z = (ac − bd) + (ad + bc)i
-- The magnitude of a complex number is √
-a
-2 + b
-2
+- Complex numbers take the form z = a + bi, where i = &radic;−1 and a and b are real. a is called the real part, b is called the imaginary part.
+- If w = c + di, then  
+  – w + z = (a + c) + (b + d)i, 
+  – w − z = (a − c) + (b − d)i, and 
+  – w × z = (ac − bd) + (ad + bc)i 
+- The magnitude of a complex number is &radic;a<sup>2</sup> + b<sup>2</sup>;
 
 ## 14.2 Complex Class declaration (complex.h)
 
 ```cpp
 class Complex {
 public:
-Complex(double x=0, double y=0) : real_(x), imag_(y) {} // default constructor
-Complex(Complex const& old) : real_(old.real_), imag_(old.imag_) {} // copy constructor
-Complex& operator= (Complex const& rhs); // Assignment operator
-double Real() const { return real_; }
-void SetReal(double x) { real_ = x; }
-double Imaginary() const { return imag_; }
-void SetImaginary(double y) { imag_ = y; }
-double Magnitude() const { return sqrt(real_*real_ + imag_*imag_); }
-Complex operator+ (Complex const& rhs) const;
-Complex operator- () const; // unary operator- negates a complex number
-friend istream& operator>> (istream& istr, Complex& c);
+	Complex(double x=0, double y=0) : real_(x), imag_(y) {} // default constructor
+	Complex(Complex const& old) : real_(old.real_), imag_(old.imag_) {} // copy constructor
+	Complex& operator= (Complex const& rhs); // Assignment operator
+	double Real() const { return real_; }
+	void SetReal(double x) { real_ = x; }
+	double Imaginary() const { return imag_; }
+	void SetImaginary(double y) { imag_ = y; }
+	double Magnitude() const { return sqrt(real_*real_ + imag_*imag_); }
+	Complex operator+ (Complex const& rhs) const;
+	Complex operator- () const; // unary operator- negates a complex number
+	friend istream& operator>> (istream& istr, Complex& c);
 private:
-double real_, imag_;
+	double real_, imag_;
 };
 Complex operator- (Complex const& left, Complex const& right); // non-member function
 ostream& operator<< (ostream& ostr, Complex const& c); // non-member function
@@ -45,34 +39,34 @@ ostream& operator<< (ostream& ostr, Complex const& c); // non-member function
 ```cpp
 // Assignment operator
 Complex& Complex::operator= (Complex const& rhs) {
-real_ = rhs.real_;
-imag_ = rhs.imag_;
-return *this;
+	real_ = rhs.real_;
+	imag_ = rhs.imag_;
+	return *this;
 }
 // Addition operator as a member function.
 Complex Complex::operator+ (Complex const& rhs) const {
-double re = real_ + rhs.real_;
-double im = imag_ + rhs.imag_;
-return Complex(re, im);
+	double re = real_ + rhs.real_;
+	double im = imag_ + rhs.imag_;
+	return Complex(re, im);
 }
 // Subtraction operator as a non-member function.
 Complex operator- (Complex const& lhs, Complex const& rhs) {
-return Complex(lhs.Real()-rhs.Real(), lhs.Imaginary()-rhs.Imaginary());
+	return Complex(lhs.Real()-rhs.Real(), lhs.Imaginary()-rhs.Imaginary());
 }
 // Unary negation operator. Note that there are no arguments.
 Complex Complex::operator- () const {
-return Complex(-real_, -imag_);
+	return Complex(-real_, -imag_);
 }
 // Input stream operator as a friend function
 istream& operator>> (istream & istr, Complex & c) {
-istr >> c.real_ >> c.imag_;
-return istr;
+	istr >> c.real_ >> c.imag_;
+	return istr;
 }
 // Output stream operator as an ordinary non-member function
 ostream& operator<< (ostream & ostr, Complex const& c) {
-if (c.Imaginary() < 0) ostr << c.Real() << " - " << -c.Imaginary() << " i ";
-else ostr << c.Real() << " + " << c.Imaginary() << " i ";
-return ostr;
+	if (c.Imaginary() < 0) ostr << c.Real() << " - " << -c.Imaginary() << " i ";
+	else ostr << c.Real() << " + " << c.Imaginary() << " i ";
+	return ostr;
 }
 ```
 
@@ -140,8 +134,8 @@ area of the declaration of Foo.
 ```cpp
 class Foo {
 public:
-friend class Bar;
-...
+	friend class Bar;
+	...
 };
 ```
 This allows member functions in class Bar to access all of the private member functions and variables of a Foo