**π‘ Problem Formulation:** In Python, modifying the imaginary part of a complex number while preserving the real part is not as straightforward as it might seem. Users often require an approach to change only the imaginary part without affecting the real part. For example, if you have a complex number `3+4j`

, and you want to change it to `3+5j`

, what would be the most efficient and Pythonic way to do so?

## Method 1: Using Complex Number Arithmetic

This method modifies the imaginary part of a complex number by subtracting the original imaginary part and adding the new one. The arithmetic operation ensures that the real part remains unchanged while the imaginary part is updated appropriately.

Here’s an example:

original_complex = 3 + 4j new_imaginary = 5 result = original_complex - (original_complex.imag * 1j) + (new_imaginary * 1j) print(result)

Output:

(3+5j)

This code creates a complex number, then subtracts the original imaginary part multiplied by the imaginary unit and adds the new imaginary component, also multiplied by the imaginary unit. This method relies on Python’s built-in support for complex numbers and arithmetic operations, making it straightforward to understand and implement.

## Method 2: Using the `complex()`

Function

The `complex()`

function in Python can be used to generate a new complex number by specifying the real and imaginary parts. This method is clean and direct, wherein you can explicitly assign the real and imaginary parts to construct the updated complex number.

Here’s an example:

original_complex = 3 + 4j new_imaginary = 5 result = complex(original_complex.real, new_imaginary) print(result)

Output:

(3+5j)

This snippet takes advantage of the `complex()`

function, which is a built-in Python function designed to create complex numbers. By keeping the real part as is from the original number and specifying a new imaginary part, this method creates a new complex number with the desired properties.

## Method 3: Using Object Attributes

Complex numbers in Python are objects with real and imag attributes which reflect their respective parts. This method shows how to create a new complex number by accessing these attributes directly and constructing a new complex number with the modified imaginary part.

Here’s an example:

original_complex = 3 + 4j new_imaginary = 5 result = complex(original_complex.real, new_imaginary) print(result)

Output:

(3+5j)

In the example, we’re directly accessing the real part of the complex number using `original_complex.real`

and then creating a new complex number by combining it with the new imaginary part. This approach is both readable and efficient, as it uses the built-in attributes of complex number objects.

## Method 4: Using a Custom Function

If you frequently need to change the imaginary part of a complex number, encapsulating the logic in a function is a practical approach. This method allows for code reuse and abstraction, making the overall codebase cleaner and more maintainable.

Here’s an example:

def change_imaginary(complex_num, new_imag): return complex(complex_num.real, new_imag) original_complex = 3 + 4j new_imaginary = 5 result = change_imaginary(original_complex, new_imaginary) print(result)

Output:

(3+5j)

In this code snippet, we define a function called `change_imaginary`

which takes a complex number and a new imaginary value as arguments and returns a new complex number with the updated imaginary part. It’s a clean and reusable way to perform this operation in a more structured codebase.

## Bonus One-Liner Method 5: Using a Lambda Function

For those who enjoy concise and inline solutions, a lambda function can be used as an on-the-fly tool to change the imaginary part of a complex number.

Here’s an example:

original_complex = 3 + 4j new_imaginary = 5 change_imaginary = lambda c, i: complex(c.real, i) result = change_imaginary(original_complex, new_imaginary) print(result)

Output:

(3+5j)

This snippet defines a lambda function that behaves similarly to the custom function we’ve previously defined, but in a more compact form. It is a one-liner that you could use in a script without defining a whole new function, useful for simple and quick tasks.

## Summary/Discussion

**Method 1:**Complex Number Arithmetic. Easy to understand if familiar with complex numbers. Can be less readable due to arithmetic manipulation.**Method 2:**Using`complex()`

Function. Very readable and straightforward. Could be considered less efficient if only the imaginary part needs to be changed often.**Method 3:**Using Object Attributes. Direct and clear. May be confused with actual attribute assignment, which is not possible with built-in complex types.**Method 4:**Using a Custom Function. Enhances code reusability and readability, especially in larger codebases. Slightly more verbose for one-off tasks.**Bonus Method 5:**Using a Lambda Function. Compact and handy for scripting. Less readable for users not familiar with lambda functions or Python ternary operations.