Complex type in R Programming - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of complex number arithmetic

What is the output of this R code when adding two complex numbers?

R Programming

z1 <- 3 + 4i
z2 <- 1 - 2i
result <- z1 + z2
print(result)

A 4+2i

B 2+6i

C 4-2i

D 4+6i

💡 Hint

Remember to add real parts and imaginary parts separately.

Adding complex numbers means adding their real parts and imaginary parts separately: (3+1) + (4-2)i = 4+2i.

❓ Predict Output

intermediate

Result of complex conjugate function

What does the following R code print?

R Programming

z <- 5 - 7i
conj_z <- Conj(z)
print(conj_z)

A 5+7i

B 5-7i

C -5+7i

D -5-7i

💡 Hint

The conjugate of a complex number flips the sign of the imaginary part.

The conjugate of 5 - 7i is 5 + 7i because only the imaginary part changes sign.

❓ Predict Output

advanced

Output of complex division

What is the output of this R code dividing two complex numbers?

R Programming

z1 <- 2 + 3i
z2 <- 1 - 1i
result <- z1 / z2
print(round(result, 2))

A 2.5-0.5i

B 2.5+0.5i

C -0.5+2.5i

D 0.5-2.5i

💡 Hint

Divide complex numbers by multiplying numerator and denominator by the conjugate of the denominator.

Dividing (2+3i) by (1-1i) results in (-0.5+2.5i) after simplification.

🧠 Conceptual

advanced

Understanding complex number modulus

What does the R function Mod() return when applied to a complex number?

A The angle (in radians) of the complex number

B The real part of the complex number

C The imaginary part of the complex number

D The magnitude (distance from origin) of the complex number

💡 Hint

Think about how far the point is from zero on the complex plane.

Mod() returns the magnitude or absolute value of the complex number, which is the distance from the origin.

🔧 Debug

expert

Identify the error in complex number creation

Which option will cause an error when trying to create a complex number in R?

R Programming

z <- complex(real = 3, imaginary = 4)

A complex(real = 3, imaginary = 4)

B complex(real = 3, imag = 4)

C complex(real = 3, imaginary = 4i)

D complex(real = 3, imaginary = "4")

💡 Hint

Check the exact argument names for the complex() function in R.

The argument 'imag' does not exist; the correct argument name is 'imaginary'. Using 'imag' causes an error.