Complex numbers in MATLAB - Mini Project: Build & Apply

Working with Complex Numbers in MATLAB

📖 Scenario: You are working on a simple electrical engineering problem where voltages and currents are represented as complex numbers. You need to create and manipulate complex numbers in MATLAB to find their magnitudes and phases.

🎯 Goal: Build a MATLAB script that creates complex numbers, calculates their magnitudes and phases, and displays the results.

📋 What You'll Learn

Create complex numbers using real and imaginary parts

Calculate magnitude using MATLAB's abs function

Calculate phase (angle) using MATLAB's angle function

Display results clearly using disp

💡 Why This Matters

🌍 Real World

Complex numbers are used in electrical engineering to represent voltages and currents that have both magnitude and phase.

💼 Career

Understanding complex numbers and how to manipulate them in MATLAB is important for engineers working with signals, circuits, and control systems.

1

Create complex numbers

Create two complex numbers called z1 and z2 with these exact values: z1 = 3 + 4i and z2 = 1 - 2i.

MATLAB

% Create complex numbers z1 and z2
% Your code here

Hint

Use i to represent the imaginary unit in MATLAB.

2

Calculate magnitudes

Create two variables called mag1 and mag2 that store the magnitudes of z1 and z2 using the abs function.

MATLAB

z1 = 3 + 4i;
z2 = 1 - 2i;
% Calculate magnitudes mag1 and mag2
% Your code here

Hint

Use abs(z) to get the magnitude of a complex number z.

3

Calculate phases

Create two variables called phase1 and phase2 that store the phases (angles) of z1 and z2 using the angle function.

MATLAB

z1 = 3 + 4i;
z2 = 1 - 2i;
mag1 = abs(z1);
mag2 = abs(z2);
% Calculate phases phase1 and phase2
% Your code here

Hint

Use angle(z) to get the phase of a complex number z.

4

Display results

Use disp to print the magnitudes and phases of z1 and z2 with clear messages exactly as shown:
"Magnitude of z1: " followed by mag1
"Phase of z1: " followed by phase1
"Magnitude of z2: " followed by mag2
"Phase of z2: " followed by phase2.

MATLAB

z1 = 3 + 4i;
z2 = 1 - 2i;
mag1 = abs(z1);
mag2 = abs(z2);
phase1 = angle(z1);
phase2 = angle(z2);
% Display magnitudes and phases
% Your code here

Hint

Use disp(['text', num2str(value)]) to display text and numbers together.

Practice

1. Which of the following correctly represents a complex number with real part 3 and imaginary part 4 in MATLAB?

easy

A. 3 + 4

B. 3i + 4

C. 3 + 4i

D. 3 + 4j + 1

Solution

1. Step 1: Understand complex number format in MATLAB

   Complex numbers are written as real part plus imaginary part times i or j, e.g., 3 + 4i.

2. Step 2: Check each option

   3 + 4i uses 3 + 4i which is correct. 3 + 4 misses imaginary part. 3i + 4 swaps real and imaginary incorrectly. 3 + 4j + 1 adds extra 1.

3. Final Answer:

   3 + 4i -> Option C

4. Quick Check:

   Complex number = 3 + 4i [OK]

Hint: Use 'i' or 'j' after the imaginary part number [OK]

Common Mistakes:

• Forgetting to include 'i' or 'j' for imaginary part
• Swapping real and imaginary parts
• Adding extra numbers outside complex format

2. Which of the following MATLAB commands correctly creates a complex number variable named z with real part 5 and imaginary part -2?

easy

A. z = complex(5, -2);

B. z = 5 + 2i;

C. z = 5 + -2;

D. z = 5 - 2;

Solution

1. Step 1: Recall MATLAB syntax for complex numbers

   Using complex(real, imag) function is a clear way to create complex numbers.

2. Step 2: Analyze options

   z = 5 - 2; is just a real number. z = 5 + 2i; creates 5 + 2i (wrong imaginary part). z = 5 + -2; is a real number. z = complex(5, -2); uses complex(5, -2) correctly.

3. Final Answer:

   z = complex(5, -2); -> Option A

4. Quick Check:

   complex(5, -2) creates correct complex number [OK]

Hint: Use complex(real, imag) for clear complex number creation [OK]

Common Mistakes:

• Writing imaginary part without 'i' or 'j'
• Using wrong sign for imaginary part
• Confusing syntax of complex() function

3. What is the output of the following MATLAB code?

z1 = 2 + 3i;
z2 = 1 - 4i;
result = z1 * z2;

medium

A. 10 - 5i

B. 14 - 5i

C. 14 + 5i

D. 10 + 5i

Solution

1. Step 1: Multiply complex numbers (a+bi)(c+di)

   Use formula: (ac - bd) + (ad + bc)i. Here a=2, b=3, c=1, d=-4.

2. Step 2: Calculate real and imaginary parts

   Real: 2*1 - 3*(-4) = 2 + 12 = 14. Imaginary: 2*(-4) + 3*1 = -8 + 3 = -5. So result = 14 - 5i.

3. Final Answer:

   14 - 5i -> Option B

4. Quick Check:

   (2+3i)*(1-4i) = 14 - 5i [OK]

Hint: Multiply using (ac - bd) + (ad + bc)i formula [OK]

Common Mistakes:

• Mixing signs in multiplication
• Forgetting to multiply imaginary parts by i^2 = -1
• Adding instead of subtracting real parts

4. Identify the error in the following MATLAB code snippet:

z = 4 + 5k;
disp(z);

medium

A. Variable 'k' is undefined, should use 'i' or 'j' for imaginary unit

B. Missing semicolon after assignment

C. disp() cannot display complex numbers

D. Real part must be negative

Solution

1. Step 1: Check imaginary unit usage in MATLAB

   MATLAB uses 'i' or 'j' for imaginary unit, 'k' is not recognized.

2. Step 2: Analyze code error

   Using '5k' causes an undefined variable error. Semicolon is optional. disp() works with complex numbers. Real part can be any number.

3. Final Answer:

   Variable 'k' is undefined, should use 'i' or 'j' for imaginary unit -> Option A

4. Quick Check:

   Imaginary unit must be 'i' or 'j' [OK]

Hint: Use only 'i' or 'j' for imaginary unit in MATLAB [OK]

Common Mistakes:

• Using undefined letters for imaginary unit
• Assuming semicolon is mandatory
• Thinking disp() can't show complex numbers

5. You have two complex numbers a = 3 + 4i and b = 2 - 4i. Write MATLAB code to compute the magnitude of their sum and select the correct output.

sum_ab = a + b;
mag = abs(sum_ab);
disp(mag);

hard

A. 7

B. 4

C. 3

D. 5

Solution

1. Step 1: Calculate sum of complex numbers

   a + b = (3 + 2) + (4 - 4)i = 5 + 0i.

2. Step 2: Calculate magnitude using abs()

   Magnitude = sqrt(5^2 + 0^2) = sqrt(25) = 5.

3. Step 3: Check output of disp(mag)

   MATLAB displays 5.

4. Final Answer:

   5 -> Option D

5. Quick Check:

   abs(5 + 0i) = 5 [OK]

Hint: Use abs() to get magnitude of complex number [OK]

Common Mistakes:

• Adding magnitudes instead of complex numbers
• Forgetting to use abs() for magnitude
• Calculating magnitude incorrectly