Complex numbers in MATLAB - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of complex number multiplication

What is the output of the following MATLAB code?

MATLAB

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

A 3 + 8i

B 11 + 2i

C 11 - 2i

D 7 + 10i

💡 Hint

Recall how to multiply complex numbers: (a+bi)(c+di) = (ac - bd) + (ad + bc)i.

Multiplying (3+4i) and (1-2i) gives (3*1 - 4* -2) + (3* -2 + 4*1)i = (3 + 8) + (-6 + 4)i = 11 - 2i.

🧠 Conceptual

intermediate

Understanding complex conjugate in MATLAB

Which MATLAB expression correctly computes the complex conjugate of z = 5 + 6i?

A abs(5 + 6i)

B conj(5 + 6i)

C real(5 + 6i)

D imag(5 + 6i)

💡 Hint

The complex conjugate flips the sign of the imaginary part.

The MATLAB function conj() returns the complex conjugate, which changes 5+6i to 5-6i.

🔧 Debug

advanced

Identify the error in complex number addition

What error does the following MATLAB code produce?

MATLAB

z1 = 2 + 3i;
z2 = 4 + 5j;
result = z1 + z2;
disp(result);

A No error, output is 6 + 8i

B No error, output is 6 + 8j

C Error: Undefined function or variable 'j'

D Error: Complex number notation mismatch

💡 Hint

In MATLAB, both i and j represent the imaginary unit by default.

MATLAB treats both i and j as the imaginary unit unless they are redefined. So adding 2+3i and 4+5j works fine, resulting in 6+8i.

📝 Syntax

advanced

Correct syntax for creating a complex number

Which option correctly creates a complex number with real part 7 and imaginary part -9 in MATLAB?

A z = complex(7, -9);

B z = 7 - 9i;

C z = 7 + (-9)i;

D z = 7 - 9j;

💡 Hint

The complex() function takes two arguments: real and imaginary parts.

Option A uses the complex() function correctly. Option A is valid MATLAB syntax; MATLAB accepts it but option A is the most explicit and error-free. Option A is invalid syntax. Option A uses j which is valid but option A is the safest and clearest.

🚀 Application

expert

Calculate magnitude and phase of a complex number

Given z = -3 + 4i, what are the magnitude and phase (in radians) computed by MATLAB's abs() and angle() functions?

MATLAB

z = -3 + 4i;
magnitude = abs(z);
phase = angle(z);
disp([magnitude, phase]);

A [1, 0.7854]

B [7, 0.9273]

C [5, -0.9273]

D [5, 2.2143]

💡 Hint

Magnitude is sqrt(real^2 + imag^2). Phase is the angle from the positive real axis.

Magnitude = sqrt((-3)^2 + 4^2) = 5. Phase = atan2(4, -3) ≈ 2.2143 radians (in second quadrant).