Getting Fourier Transform from Phase and Magnitude - Matlab

The magnitude and phase of a fourier transform F are defined as:

Mag = sqrt(Real(F)^2 + Imaginary(F)^2)

and

Phase = arctan(Imaginary(F)/Real(F))

Ive tried to write matlab code that takes in a grayscale image matrix, performs fft2() on the matrix and then calculates the magnitude and phase from the transform. I then wish to calculate the imaginary and real parts of the fourier transform. This is done by rearranging the first two equations into:

Real = Mag/sqrt(1 + tan(Phase)^2)

and

Imaginary = Real*tan(Phase)

and finally combining and inverse fft2:

F = Real + i*Imaginary
image = ifft2(F)

I'd expect to see the same image as the input, but i get garbage. Is my maths wrong? My matlab mfile code is as follows:

function y = forwardBackwardFFT(image)

F = fft2(image);
mag = sqrt(real(F).^2 + imag(F).^2);
phase = atan(imag(F)./real(F));

re = sqrt((mag.^2)./(1 + tan(phase).^2));
im = re.*tan(phase);
F = re + i*im;
f = ifft2(F);

subplot(1,2,1);
imshow(image);
Title('Original Image');

subplot(1,2,2);
imshow(f);
Title('Image after forward and backward FFT');
y = f;

thanks a lot :)