sqrt(Re(z)**2 + Im(z)**2)

for z = a + ib this becomes:

sqrt(a*a + b*b)

It's just the euclidean norm. You have to sum the square of real part and imaginary part (without the i) and do the sqrt of it.

https://www.varsitytutors.com/hotmath/hotmath_help/topics/absolute-value-complex-number

Basically, two steps would be involved :

• Offset all numbers by the minimum along real and imaginary axes.

• Divide each by the max. magnitude. To get the magnitude of a complex number, simply use np.abs().

Thus, the implementation would be -

def normalize_complex_arr(a):
    a_oo = a - a.real.min() - 1j*a.imag.min() # origin offsetted
    return a_oo/np.abs(a_oo).max()

Sample runs for verification

Let'start with an array that has a minimum one of [0+0j] and two more elements - [x1+y1*J] & [y1+x1*J]. Thus, their magnitudes after normalizing should be 1 each.

In [358]: a = np.array([0+0j, 1+17j, 17+1j])

In [359]: normalize_complex_arr(a)
Out[359]: 
array([ 0.00000000+0.j        ,  0.05872202+0.99827437j,
        0.99827437+0.05872202j])

In [360]: np.abs(normalize_complex_arr(a))
Out[360]: array([ 0.,  1.,  1.])

Next up, let's add an offset to the minimum element. This shouldn't change their magnitudes after normalization -

In [361]: a = np.array([0+0j, 1+17j, 17+1j]) + np.array([2+3j])

In [362]: a
Out[362]: array([  2. +3.j,   3.+20.j,  19. +4.j])

In [363]: normalize_complex_arr(a)
Out[363]: 
array([ 0.00000000+0.j        ,  0.05872202+0.99827437j,
        0.99827437+0.05872202j])

In [364]: np.abs(normalize_complex_arr(a))
Out[364]: array([ 0.,  1.,  1.])

Finally, let's add another element that is at twice the distance from offsetted origin to make sure this new one has a magnitude of 1 and others are reduce to 0.5 -

In [365]: a = np.array([0+0j, 1+17j, 17+1j, 34+2j]) + np.array([2+3j])

In [366]: a
Out[366]: array([  2. +3.j,   3.+20.j,  19. +4.j,  36. +5.j])

In [367]: normalize_complex_arr(a)
Out[367]: 
array([ 0.00000000+0.j        ,  0.02936101+0.49913719j,
        0.49913719+0.02936101j,  0.99827437+0.05872202j])

In [368]: np.abs(normalize_complex_arr(a))
Out[368]: array([ 0. ,  0.5,  0.5,  1. ])

Just use np.abs:

>>> a = np.array([1+2j, 3+4j])
>>> np.abs(a)
array([2.23606798, 5.        ])