Complex numbers in MATLAB - Interactive Code Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to create a complex number with real part 3 and imaginary part 4.

MATLAB

z = 3 + [1] * 4;

Drag options to blanks, or click blank then click option'

Aj

Bi

Ck

Dm

Attempts:

3 left

💡 Hint

Common Mistakes

Using a variable other than i or j for the imaginary unit.

Forgetting to multiply the imaginary unit by the imaginary part.

In MATLAB, the imaginary unit is commonly represented by j or i. Here, j is used.

2fill in blank

medium

Complete the code to calculate the magnitude of the complex number z.

MATLAB

magnitude = [1](z);

Drag options to blanks, or click blank then click option'

Aabs

Bmag

Cmod

Dlength

Attempts:

3 left

💡 Hint

Common Mistakes

Using length which returns the size of an array, not magnitude.

Using mod which is for modulus operation on integers.

The abs function in MATLAB returns the magnitude (or absolute value) of a complex number.

3fill in blank

hard

Fix the error in the code to get the phase angle of the complex number z.

MATLAB

angle_value = [1](z);

Drag options to blanks, or click blank then click option'

Aphase

Batan

Carg

Dangle

Attempts:

3 left

💡 Hint

Common Mistakes

Using phase which is not a MATLAB function.

Using arg which is not recognized in MATLAB.

The MATLAB function angle returns the phase angle (in radians) of a complex number.

4fill in blank

hard

Fill both blanks to create a complex number from magnitude 5 and angle pi/4.

MATLAB

z = [1] * (cos([2]) + 1i * sin(pi/4));

Drag options to blanks, or click blank then click option'

A5

Bpi/4

Cpi/2

D3

Attempts:

3 left

💡 Hint

Common Mistakes

Using the wrong angle value inside cosine and sine.

Confusing magnitude with angle.

The complex number in polar form is magnitude times (cos(angle) + i*sin(angle)). Here, magnitude is 5 and angle is pi/4.

5fill in blank

hard

Fill all three blanks to create a vector of complex numbers with real parts 1 to 3 and imaginary parts 4 to 6.

MATLAB

z = [1] + [2] * [3];

Drag options to blanks, or click blank then click option'

A1:3

B1i

C4:6

D1j

Attempts:

3 left

💡 Hint

Common Mistakes

Using 1j instead of 1i (both work but only one is correct here).

Mixing up the ranges for real and imaginary parts.

The vector z is created by adding the real parts 1:3 to the imaginary parts 4:6 multiplied by the imaginary unit 1i.

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