Complex number type in NumPy - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of numpy complex array addition

What is the output of this code that adds two numpy arrays of complex numbers?

NumPy

import numpy as np
arr1 = np.array([1+2j, 3+4j])
arr2 = np.array([5+6j, 7+8j])
result = arr1 + arr2
print(result)

A array([6.+6.j, 10.+12.j])

B array([6.+8.j, 10.+10.j])

C array([6.+8.j, 10.+12.j])

D array([6.+8.j, 10.+14.j])

💡 Hint

Remember how complex numbers add: real parts add, imaginary parts add.

Adding complex numbers adds their real parts and imaginary parts separately. So (1+2j)+(5+6j) = (1+5)+(2+6)j = 6+8j, similarly for the second element.

❓ data_output

intermediate

Shape and dtype of complex numpy array

What is the shape and data type of this numpy array?

NumPy

import numpy as np
arr = np.array([[1+1j, 2+2j], [3+3j, 4+4j]])
print(arr.shape, arr.dtype)

A (2, 2) complex128

B (4,) complex128

C (2, 2) complex64

D (2, 2) float64

💡 Hint

Check the shape of the nested list and default complex dtype in numpy.

The array is 2 rows by 2 columns, so shape is (2, 2). By default, numpy uses complex128 for complex numbers.

🔧 Debug

advanced

Identify the error in complex number array creation

What error does this code raise when trying to create a numpy array of complex numbers?

NumPy

import numpy as np
arr = np.array([1+2, 3+4j])

A No error, creates array with dtype complex128

B No error, creates array with mixed types

C ValueError: setting an array element with a sequence

D TypeError: unsupported operand type(s) for +: 'int' and 'int'

💡 Hint

Check how numpy handles mixed numeric types including complex and int.

Numpy converts all elements to a common type that can hold all values. Here, int 1+2 is just 3, so array becomes [3, 3+4j] and dtype complex128.

❓ visualization

advanced

Visualizing real and imaginary parts of complex array

Which option correctly plots the real and imaginary parts of this complex numpy array?

NumPy

import numpy as np
import matplotlib.pyplot as plt
arr = np.array([1+2j, 3+4j, 5+6j])
plt.plot(arr.real, label='Real')
plt.plot(arr.imag, label='Imaginary')
plt.legend()
plt.show()

A Scatter plot with points at (1,2), (3,4), (5,6)

B Pie chart showing ratio of real to imaginary parts

C Bar chart with bars for magnitude of each complex number

D Line plot with two lines: real parts [1,3,5] and imaginary parts [2,4,6]

💡 Hint

Look at what plt.plot(arr.real) and plt.plot(arr.imag) produce.

The code plots two lines: one for the real parts and one for the imaginary parts of the complex array elements.

🧠 Conceptual

expert

Effect of numpy complex dtype on arithmetic precision

Which statement about numpy complex dtypes is correct?

A complex128 uses 64 bits total, 32 bits each for real and imaginary parts

B complex64 uses 32 bits for real and 32 bits for imaginary parts, offering less precision than complex128

C complex64 and complex128 have the same precision but differ in memory layout

D complex128 uses 128 bits for the real part only, imaginary part is stored separately

💡 Hint

Recall how floating point precision relates to complex number storage.

complex64 stores two 32-bit floats (real and imaginary), while complex128 stores two 64-bit floats, so complex128 has higher precision.