Complex number type in NumPy - Step-by-Step Execution

Concept Flow - Complex number type

Create complex number

↓

Store in numpy array

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Access real and imaginary parts

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Perform operations (add, multiply)

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Get magnitude and angle

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Use results for analysis or visualization

This flow shows how to create, manipulate, and analyze complex numbers using numpy arrays step-by-step.

Execution Sample

NumPy

import numpy as np
z = np.array([1+2j, 3+4j])
real = z.real
imag = z.imag
mag = np.abs(z)
angle = np.angle(z)

Create a numpy array of complex numbers, then extract real, imaginary parts, magnitude, and angle.

Execution Table

Step	Code Line	Variable	Value	Explanation
1	z = np.array([1+2j, 3+4j])	z	[1.+2.j 3.+4.j]	Create numpy array with two complex numbers
2	real = z.real	real	[1. 3.]	Extract real parts of each complex number
3	imag = z.imag	imag	[2. 4.]	Extract imaginary parts of each complex number
4	mag = np.abs(z)	mag	[2.23606798 5.]	Calculate magnitude (distance from origin)
5	angle = np.angle(z)	angle	[1.10714872 0.92729522]	Calculate angle (phase) in radians
6	End	-	-	All variables computed successfully

💡 Execution ends after computing magnitude and angle for all complex numbers.

Variable Tracker

Variable	Start	After Step 1	After Step 2	After Step 3	After Step 4	After Step 5	Final
z	undefined	[1.+2.j 3.+4.j]	[1.+2.j 3.+4.j]	[1.+2.j 3.+4.j]	[1.+2.j 3.+4.j]	[1.+2.j 3.+4.j]	[1.+2.j 3.+4.j]
real	undefined	undefined	[1. 3.]	[1. 3.]	[1. 3.]	[1. 3.]	[1. 3.]
imag	undefined	undefined	undefined	[2. 4.]	[2. 4.]	[2. 4.]	[2. 4.]
mag	undefined	undefined	undefined	undefined	[2.23606798 5.]	[2.23606798 5.]	[2.23606798 5.]
angle	undefined	undefined	undefined	undefined	undefined	[1.10714872 0.92729522]	[1.10714872 0.92729522]

Key Moments - 3 Insights

Why does z.real return an array of real parts instead of a single number?

Because z is an array of complex numbers, z.real returns the real part of each element, as shown in execution_table step 2.

What does np.abs(z) compute for complex numbers?

np.abs(z) computes the magnitude (distance from origin) of each complex number, not just the absolute value of real or imaginary parts, as seen in step 4.

Why is the angle returned in radians and not degrees?

np.angle returns the phase angle in radians by default, which is standard in numpy and math libraries, as shown in step 5.

Visual Quiz - 3 Questions

Look at the execution table at step 3. What is the value of 'imag'?

A [1. 3.]

B [2.23606798 5.]

C [2. 4.]

D [1.+2.j 3.+4.j]

💡 Hint

Check the 'imag' variable value in the row for step 3 in the execution_table.

At which step does the variable 'mag' get its value?

A Step 4

B Step 2

C Step 3

D Step 5

💡 Hint

Look for when np.abs(z) is called in the execution_table.

If we change z to np.array([2+0j, 0+3j]), what would be the magnitude of the first element?

A 3.0

B 2.0

C 0.0

D 5.0

💡 Hint

Magnitude is the distance from origin, calculated as sqrt(real^2 + imag^2).

Concept Snapshot

Complex number type in numpy:
- Use np.array([a+bj, ...]) to create complex arrays
- Access real parts with .real, imaginary with .imag
- Use np.abs() for magnitude, np.angle() for phase
- Angles are in radians
- Useful for signal processing, physics, and engineering

Full Transcript

This lesson shows how to work with complex numbers in numpy. First, we create a numpy array with complex numbers. Then, we extract the real and imaginary parts separately. Next, we calculate the magnitude using np.abs, which gives the distance from zero in the complex plane. We also find the angle or phase using np.angle, which returns the angle in radians. These steps help analyze complex data in many fields. The execution table traces each step and variable value. Key moments clarify common confusions about array operations and angle units. The quiz tests understanding of variable values and calculations. The snapshot summarizes the main points for quick review.