Complex number type in NumPy

Introduction

Complex numbers help us work with values that have a real and an imaginary part. They are useful in many science and engineering problems.

When dealing with electrical circuits that use alternating current.

When analyzing waves or signals in physics or engineering.

When solving equations that have no real number solutions.

When working with Fourier transforms in data analysis.

When modeling rotations and oscillations in 2D space.

Syntax

NumPy

numpy.complex64
numpy.complex128

# Create a complex number array:
np.array([1+2j, 3+4j], dtype=np.complex64)

Use complex64 for single precision complex numbers (real and imaginary parts are 32-bit floats).

Use complex128 for double precision complex numbers (real and imaginary parts are 64-bit floats).

Examples

This creates a numpy array of complex numbers with single precision.

NumPy

import numpy as np
z = np.array([1+2j, 3+4j], dtype=np.complex64)
print(z)

This creates a single complex number with double precision.

NumPy

z = np.complex128(5 + 6j)
print(z)

This creates a complex array by adding real and imaginary parts separately.

NumPy

z = np.array([1, 2, 3]) + 1j * np.array([4, 5, 6])
print(z)

Sample Program

This program creates an array of complex numbers, then finds their magnitudes and angles. Magnitude tells how far the number is from zero, and angle tells the direction.

NumPy

import numpy as np

# Create a complex array
z = np.array([2+3j, 4+5j, 6+7j], dtype=np.complex128)

# Calculate the magnitude (absolute value) of each complex number
magnitudes = np.abs(z)

# Calculate the angle (phase) of each complex number
angles = np.angle(z)

print("Complex numbers:", z)
print("Magnitudes:", magnitudes)
print("Angles (radians):", angles)

Important Notes

Complex numbers in numpy always have a real and imaginary part stored as floats.

Use np.abs() to get the magnitude and np.angle() to get the angle of complex numbers.

Complex numbers can be used in many math functions like addition, multiplication, and more.

Summary

Complex numbers have a real and an imaginary part.

Use numpy's complex64 or complex128 to work with complex numbers.

You can find magnitude and angle using np.abs() and np.angle().

Practice

1. What does the numpy.complex128 data type represent?

easy

A. A string representing a complex number

B. A real number with 128 bits precision

C. An integer number with 128 bits

D. A complex number with double precision for real and imaginary parts

Solution

1. Step 1: Understand the data type name

   The name complex128 indicates a complex number type with 128 bits total.

2. Step 2: Recall complex number structure in numpy

   In numpy, complex128 stores two 64-bit floats: one for real and one for imaginary parts.

3. Final Answer:

   A complex number with double precision for real and imaginary parts -> Option D

4. Quick Check:

   complex128 = complex number with 128 bits [OK]

Hint: Look for 'complex' and bit size meaning real+imag parts [OK]

Common Mistakes:

• Confusing complex128 with real number types
• Thinking complex128 stores integers
• Assuming complex128 is a string type

2. Which of the following is the correct way to create a numpy array of complex numbers with type complex64?

easy

A. np.array([1+2j, 3+4j], dtype='complex64')

B. np.array([1+2j, 3+4j], dtype='int64')

C. np.array([1, 2, 3], dtype='complex64')

D. np.array([1+2, 3+4], dtype='complex64')

Solution

1. Step 1: Check the array elements

   The elements must be complex numbers, so they need an imaginary part like 1+2j.

2. Step 2: Check the dtype argument

   Using dtype='complex64' correctly sets the array to complex numbers with 64-bit precision.

3. Final Answer:

   np.array([1+2j, 3+4j], dtype='complex64') -> Option A

4. Quick Check:

   Complex elements + complex64 dtype = correct array [OK]

Hint: Use complex literals with 'j' and set dtype to complex64 [OK]

Common Mistakes:

• Using integer dtype with complex numbers
• Missing imaginary part in elements
• Using invalid dtype strings

3. What is the output of this code?

import numpy as np
z = np.array([3+4j, 1-1j], dtype=np.complex128)
magnitudes = np.abs(z)
print(magnitudes)

medium

A. [5. 1.41421356]

B. [7.+0.j 0.+0.j]

C. [3.+4.j 1.-1.j]

D. [0.6 0.8]

Solution

1. Step 1: Understand np.abs on complex array

   np.abs returns the magnitude (distance from origin) of each complex number.

2. Step 2: Calculate magnitudes manually

   For 3+4j, magnitude = sqrt(3^2 + 4^2) = 5. For 1-1j, magnitude = sqrt(1^2 + (-1)^2) = sqrt(2) ≈ 1.41421356.

3. Final Answer:

   [5. 1.41421356] -> Option A

4. Quick Check:

   Magnitude = sqrt(real² + imag²) [OK]

Hint: Magnitude = sqrt(real² + imag²) using np.abs [OK]

Common Mistakes:

• Confusing magnitude with real or imaginary parts
• Expecting complex output instead of float magnitudes
• Using np.angle instead of np.abs

4. The following code throws an error. What is the cause?

import numpy as np
z = np.array([1+2j, 3+4j], dtype='complex64')
angle = np.angle(z, deg=True)
print(angle)

medium

A. np.angle does not support degree output

B. No error; code runs fine

C. Missing import for np.angle function

D. dtype 'complex64' is invalid for np.angle

Solution

1. Step 1: Check dtype compatibility

   np.angle works with complex arrays of any valid complex dtype including complex64.

2. Step 2: Check np.angle parameters

   The parameter deg=True is valid and returns angle in degrees.

3. Final Answer:

   No error; code runs fine -> Option B

4. Quick Check:

   np.angle supports complex64 and deg=True [OK]

Hint: np.angle supports complex64 and degree output [OK]

Common Mistakes:

• Assuming complex64 is unsupported by np.angle
• Thinking deg=True is invalid
• Expecting import error for np.angle

5. You have a numpy array z = np.array([1+1j, 0+0j, -1-1j], dtype=np.complex128). You want to create a new array that contains the magnitudes but replaces zeros with the string 'zero'. Which code correctly does this?

hard

A. np.array([str(m) if m == 0 else m for m in np.abs(z)])

B. np.abs(z).replace(0, 'zero')

C. np.where(np.abs(z) == 0, 'zero', np.abs(z))

D. np.abs(z).astype(str).replace('0.0', 'zero')

Solution

1. Step 1: Calculate magnitudes with np.abs

   np.abs(z) returns an array of magnitudes as floats.

2. Step 2: Replace zeros with 'zero' using np.where

   np.where(condition, value_if_true, value_if_false) replaces elements where magnitude is 0 with string 'zero', else keeps magnitude.

3. Final Answer:

   np.where(np.abs(z) == 0, 'zero', np.abs(z)) -> Option C

4. Quick Check:

   Use np.where for conditional replacement in arrays [OK]

Hint: Use np.where(condition, 'zero', values) for replacements [OK]

Common Mistakes:

• Trying to use .replace on numpy arrays (not supported)
• Converting all to strings unnecessarily
• Using list comprehension without numpy benefits