How to calculate the explicit price matching various Bollinger band standard deviation levels?

Utilizing 1min data I want to know the exact price at which the various standard deviation levels equal that price.

Bollinger Bands commonly use 2 standard deviations and a rolling period of 20 to calculate the current level for these standard deviations. What I’m trying to do is take the previous 19 1min candles to get the 20th candle at which the close_price equals the specified standard deviation level. I want to do this to potentially determine exit/entry levels ahead of time.

Here’s what I’ve done so far in Sympy:

from sympy import Symbol, solve, sqrt, Eq
import numpy as np

def get_equal_bollinger_bands(df, stdev_list = [0, 0.5, 1, 1.5, 2, 2.5, 3,3.5,4,4.5,5,5.5]):
    matching_prices_dict = {}
    for stdev_ in stdev_list:
        stddev_level_list = [stdev_, -stdev_]

        if (stdev_ == 0):
            stddev_level_list = [0]

        for stddev_level in stddev_level_list:
            matching_price = Symbol("matching_price")
            twenty_sma = Symbol("twenty_sma")
            stdev = Symbol("stdev")

            temp_list = df[-20:-1]["close"].to_list()

            temp_list.append(matching_price)

            stdev_list = []
            for close_price in temp_list:
                stdev_list.append((close_price - twenty_sma)**2)

            eq1 = Eq(np.array(temp_list).sum()/20, twenty_sma)
            eq2 = Eq(sqrt(np.array(stdev_list).sum()/20), stdev)

            eq3 = Eq(twenty_sma + (stddev_level * stdev), matching_price)

            result = solve((eq1.simplify(), eq2.simplify(), eq3.simplify()), (matching_price, twenty_sma, stdev), dict=True)

            if (result):
                matching_prices_dict[stddev_level] = result[0][matching_price]

    return matching_prices_dict

Calling it with these values produces these standard deviation levels where the price matches:

temp_minute_list = [3923.0,
 3922.5,
 3922.5,
 3922.75,
 3922.5,
 3922.5,
 3922.25,
 3922.0,
 3922.25,
 3922.25,
 3923.0,
 3923.75,
 3923.5,
 3923.5,
 3923.0,
 3923.5,
 3923.0,
 3923.25,
 3923.25,
 3923.0]

import pandas as pd
df = pd.DataFrame(temp_minute_list, columns=["close"])

temp = get_equal_bollinger_bands(df)
temp

{0: 3922.85526315789,
0.5: 3923.11453266651,
-0.5: 3922.59599364928,
1: 3923.38449482621,
-1: 3922.32603148958,
1.5: 3923.67819890843,
-1.5: 3922.03232740736,
2: 3924.01475164942,
-2: 3921.69577466636,
2.5: 3924.42731546604,
-2.5: 3921.28321084975,
3: 3924.98537953305,
-3: 3920.72514678273,
3.5: 3925.88007409178,
-3.5: 3919.83045222400,
4: 3928.04065333026,
-4: 3917.66987298550,
4.5: 3922.85526315793 – 9.03731840154405I,
5: 3922.8552631579 – 4.58328069248354I,
5.5: 3922.8552631579 – 3.68187045988833*I}

I want to do this but I don’t want to get imaginary/complex numbers. How can I change this so that happens?

I’ve tried using,

matching_price = Symbol("matching_price", real=True)

, but that just removes the complex results.