Pandas using apply lambda with two different operators

This question is very similar to one I posted before with just one change. Instead of doing just the absolute difference for all the columns I also want to find the magnitude difference for the 'Z' column, so if the current Z is 1.1x greater than prev than keep it.

(more context to the problem)

Pandas using the previous rank values to filter out current row

df = pd.DataFrame({
    'rank': [1, 1, 2, 2, 3, 3],
    'x': [0, 3, 0, 3, 4, 2],
    'y': [0, 4, 0, 4, 5, 5],
    'z': [1, 3, 1.2, 3.25, 3, 6],
})
print(df)
#    rank  x  y     z
# 0     1  0  0  1.00
# 1     1  3  4  3.00
# 2     2  0  0  1.20
# 3     2  3  4  3.25
# 4     3  4  5  3.00
# 5     3  2  5  6.00

Here's what I want the output to be

output = pd.DataFrame({
    'rank': [1, 1, 2, 3],
    'x': [0, 3, 0, 2],
    'y': [0, 4, 0, 5],
    'z': [1, 3, 1.2, 6],
})
print(output)
#    rank  x  y    z
# 0     1  0  0  1.0
# 1     1  3  4  3.0
# 2     2  0  0  1.2
# 5     3  2  5  6.00

basically what I want to happen is if the previous rank has any rows with x, y (+- 1 both ways) AND z (<1.1x) to remove it.

So for the rows rank 1 ANY rows in rank 2 that have any combo of x = (-1-1), y = (-1-1), z= (<1.1) OR x = (2-5), y = (3-5), z= (<3.3) I want it to be removed

from Pandas using apply lambda with two different operators