Operator >> Overload

I am performing a complex number using operator overloading. In the program, the user enters a complex number ALWAYS in the form:

a + bi

So in the example ...

25.0 + 3.6i

Assume that the user will always enter both the real and imaginary parts of the complex number, for example, the user enters "5 + 0i" (rather than "5") or "0 - 6.2i" (and not "-6.2i").

My problem is that in main () I have the following code:

ComplexNumber c1;
cin >> c1;
cout << c1;

and the code prints:

0 + 0i

... when I entered "4.2 + 8.3i" at the run-time prompt.

Here is my implementation of my class operator>>:

istream & operator>>(istream & in, ComplexNumber & n) {
    string real;
    string imag;
    bool done = false;
    int sign = 1;

    string num;
    in >> num;

    int length;
    for (int i = 0; i < num.length(); i++) {
        if (num.at(i) == 'i') {
            imag = num.substr((i - length), i);
        }
        else if (num.at(i) == '-') {
            sign = -1;
        }
        else if (num.at(i) == ' ') {
            if (!done) {
                real = num.substr(i);
                done = true;
            }
            length = 0;
        }
        length++;
    }

    n = ComplexNumber(atof(real.c_str()), atof(imag.c_str()) * sign);
    return in;
}

Here is my class implementation operator<<:

ostream & operator<<(ostream & out, const ComplexNumber & n) {
    n.print(out);
    return out;
}

Here is my implementation of the ComplexNumber print () member class:

void ComplexNumber::print(ostream & out) const {
    if (imag >= 0)
        out << real << " + " << imag << "i";
    else 
        out << real << " - " << (-1 * imag) << "i";
}

This is the ComplexNumber header file for more details:

#ifndef COMPLEXNUMBER_H
#define COMPLEXNUMBER_H

#include <iostream>
using namespace std;

class ComplexNumber {

  public:

    // constructors
    ComplexNumber();
    ComplexNumber(double real_part, double imaginary_part);
    ComplexNumber(const ComplexNumber & rhs);

    // named member functions
    void print(ostream & out = cout) const;
    bool equals(const ComplexNumber & rhs) const;

    // assignment operators
    const ComplexNumber & operator=(const ComplexNumber & rhs);
    const ComplexNumber & operator+=(const ComplexNumber & rhs);
    const ComplexNumber & operator-=(const ComplexNumber & rhs);
    const ComplexNumber & operator*=(const ComplexNumber & rhs);

  private:
    double real;      
    double imag; 
};

// arithmetic operators
ComplexNumber operator+(const ComplexNumber & lhs, const ComplexNumber & rhs);
ComplexNumber operator-(const ComplexNumber & lhs, const ComplexNumber & rhs);
ComplexNumber operator*(const ComplexNumber & lhs, const ComplexNumber & rhs);

// relational operators
bool operator==(const ComplexNumber & lhs, const ComplexNumber & rhs);
bool operator!=(const ComplexNumber & lhs, const ComplexNumber & rhs);

// I/O operators
ostream & operator<<(ostream & out, const ComplexNumber & n);
istream & operator>>(istream & in, ComplexNumber & n);

#endif

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