1 | initial version |

It seems that, in your expressions, $x$ denotes a real number. If this were the case, you can get the coefficients of `I`

by taking the imaginary part of the expression:

```
sage: f = x^2 + 2*I*x + 1
sage: g = x^2 + I*x + 1
sage: h = x^2 + 2*x + I
sage: k = x^2 + x + 2*I
sage: assume(x,'real')
sage: for expression in [f, g, h, k]:
....: print(expression.imag())
2*x
x
1
2
```

2 | No.2 Revision |

**Edited.** This was the original answer

It seems that, in your expressions, $x$ denotes a real number. If this were the case, you can get the coefficients of `I`

by taking the imaginary part of the expression:

```
sage: f = x^2 + 2*I*x + 1
sage: g = x^2 + I*x + 1
sage: h = x^2 + 2*x + I
sage: k = x^2 + x + 2*I
sage: assume(x,'real')
sage: for expression in [f, g, h, k]:
....: print(expression.imag())
2*x
x
1
2
```

**New answer**. I have improved your approach, based on wildcards. It seems that `I`

is not detected because it is not a symbolic variable. So, we can temporarily transform `I`

into such a variable, find the coefficients of `I`

in the expressions and then restore `I`

:

```
w0 = SR.wild(0)
var("I")
f = x^2 + 2*I*x + 1
g = x^2 + I*x + 1
h = x^2 + 2*x + I
k = x^2 + x + 2*I
m = sqrt(1-x^2) + I*(1-x^3)^(1/3)
n = sqrt(1-x^2) + 2*I*(1-x^3)^(1/3)
p = x^2 + 2*x - I
q = x^2 + 2*x
expressions = [f, g, h, k, m, n, p, q]
for expression in expressions:
print("\nExpression: ",expression)
if expression.has(I):
if expression.has(w0*I):
aux = expression.find(w0*I)
coef = aux[0].match(w0*I)[w0]
else:
coef = 1
print(f"The coefficient of I is {coef}")
else:
print("The expression does not contain I")
restore("I")
```

This is the output:

```
Expression: 2*I*x + x^2 + 1
The coefficient of I is 2*x
Expression: I*x + x^2 + 1
The coefficient of I is x
Expression: x^2 + I + 2*x
The coefficient of I is 1
Expression: x^2 + 2*I + x
The coefficient of I is 2
Expression: (-x^3 + 1)^(1/3)*I + sqrt(-x^2 + 1)
The coefficient of I is (-x^3 + 1)^(1/3)
Expression: 2*(-x^3 + 1)^(1/3)*I + sqrt(-x^2 + 1)
The coefficient of I is 2*(-x^3 + 1)^(1/3)
Expression: x^2 - I + 2*x
The coefficient of I is -1
Expression: x^2 + 2*x
The expression does not contain I
```

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