python – implementation of complex numbers

I have this part of a code that I need to implement or modify the necessary methods in the class so that the program produces the following output.

c1 = 1+2i 
c2 = 3-4i 
c3 = -5 
c4 = 6i
c5 = -7i
c6 = 0
c1 + c2 = 4-2i
c1 - c2 = -2+6i
c1 * c2 = 11+2i 
conjugate of c1 = 1-2i

The implementation of the Complex class, representing complex number, is missing. The attributes of a complex number are, obviously, its real part and its imaginary part (floats) and do not need to be protected attributes. but I have no idea how to implement this in order to get the output above.

so far what I have:

code:

class Complex:
    def __init__(self, real, imag):
        self.real = real
        self.imag = imag

    def __str__(self):
        return str(self.real) + "+" + str(self.imag) + "i"


def main():
    c1 = Complex(1, 2)
    print("c1 =", c1)
    c2 = Complex(3, -4)
    print("c2 =", c2)
    c3 = Complex(-5, 0)
    print("c3 =", c3)
    c4 = Complex(0, 6)
    print("c4 =", c4)
    c5 = Complex(0, -7)
    print("c5 =", c5)
    c6 = Complex(0, 0)
    print("c6 =", c6)
    print("c1 + c2 =", c1 + c2)
    print("c1 - c2 =", c1 - c2)
    print("c1 * c2 =", c1 * c2)
    c7 = c1.conjugate()
    print("conjugate of c1 =", c7)

if __name__ == "__main__":
    main()

output:

c1 = 1+2i
c2 = 3+-4i
c3 = -5+0i
c4 = 0+6i
c5 = 0+-7i
c6 = 0+0i