Four-quadrant inverse tangent
P = atan2(Y,X)
Elements of P lie in the closed interval [-pi,pi], where pi is the MATLAB® floating-point representation of π. atan uses sign(Y) and sign(X) to determine the specific quadrant.
atan2(Y,X) contrasts with atan(Y/X), whose results are limited to the interval [–π/2, π/2], or the right side of this diagram.
Any complex number z = x + iy is converted to polar coordinates with
r = abs(z) theta = atan2(imag(z),real(z))
z = 4 + 3i; r = abs(z) theta = atan2(imag(z),real(z)) r = 5 theta = 0.6435
This is a common operation, so MATLAB software provides a function, angle(z), that computes theta = atan2(imag(z),real(z)).
To convert back to the original complex number
z = r * exp(i * theta) z = 4.0000 + 3.0000i