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.

Practice

1. What does the complex type in R represent?

easy

A. Only integers

B. Only real numbers without decimals

C. A number with both real and imaginary parts

D. Text strings representing numbers

Solution

1. Step 1: Understand the complex type definition

   The complex type stores numbers that have two parts: a real part and an imaginary part.

2. Step 2: Compare with other number types

   Unlike integers or real numbers, complex numbers include an imaginary component, often written with 'i'.

3. Final Answer:

   A number with both real and imaginary parts -> Option C

4. Quick Check:

   Complex type = real + imaginary parts [OK]

Hint: Complex numbers always have real and imaginary parts [OK]

Common Mistakes:

• Thinking complex numbers are only real numbers
• Confusing complex with integer or character types
• Ignoring the imaginary part

2. Which of the following is the correct way to create a complex number in R?

easy

A. complex(real = 3, imag = 4)

B. complex(3 + 4)

C. complex(3, 4i)

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

Solution

1. Step 1: Recall the correct argument names for complex()

   In R, the function complex() uses 'real' and 'imag' as argument names for the parts.

2. Step 2: Check each option's syntax

   complex(real = 3, imag = 4) is correct. complex(real = 3, imaginary = 4) is invalid because 'imaginary' is not a recognized argument. complex(3, 4i) mixes numeric and complex literal incorrectly. complex(3 + 4) is incomplete and invalid.

3. Final Answer:

   complex(real = 3, imag = 4) -> Option A

4. Quick Check:

   Use 'imag' not 'imaginary' in complex() [OK]

Hint: Use 'imag' for imaginary part in complex() [OK]

Common Mistakes:

• Using 'imaginary' instead of 'imag' argument
• Trying to mix numeric and complex literals incorrectly
• Omitting closing parentheses

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

z <- 3 + 4i
Mod(z)

medium

A. 5

B. 7

C. 12

D. 25

Solution

1. Step 1: Understand Mod() function

   Mod(z) returns the modulus (length) of the complex number z, calculated as sqrt(real^2 + imaginary^2).

2. Step 2: Calculate modulus for z = 3 + 4i

   Modulus = sqrt(3^2 + 4^2) = sqrt(9 + 16) = sqrt(25) = 5.

3. Final Answer:

   5 -> Option A

4. Quick Check:

   Modulus = sqrt(3² + 4²) = 5 [OK]

Hint: Modulus = sqrt(real² + imaginary²) [OK]

Common Mistakes:

• Adding real and imaginary parts instead of squaring
• Confusing Mod() with Arg()
• Calculating 3 + 4 instead of sqrt(3² + 4²)

4. Identify the error in this R code snippet:

z <- complex(real=2, imag=3)
Re(z)

medium

A. The argument 'imag' should be 'imaginary'

B. Re() cannot be used on complex numbers

C. Missing parentheses in Re(z)

D. complex() does not accept named arguments

Solution

1. Step 1: Check argument names in complex()

   The argument 'imag' is correct for the imaginary part in complex().

2. Step 2: Verify usage of Re()

   Re() correctly extracts the real part from a complex number, so its usage is correct.

3. Final Answer:

   Re() cannot be used on complex numbers -> Option B

4. Quick Check:

   Re() is valid for complex numbers, so no error here [Incorrect]

Hint: Use 'imag' for imaginary part, not 'imaginary' [OK]

Common Mistakes:

• Using 'imag' instead of 'imaginary'
• Thinking Re() is invalid for complex numbers
• Forgetting to close parentheses

5. Given a vector of complex numbers z <- c(1+1i, 2+2i, 3+3i), which R code correctly creates a named list with keys as the real parts and values as the imaginary parts?

hard

A. list(names = Re(z), values = Im(z))

B. setNames(as.list(Re(z)), as.character(Im(z)))

C. list(keys = Im(z), vals = Re(z))

D. setNames(as.list(Im(z)), as.character(Re(z)))

Solution

1. Step 1: Extract real and imaginary parts

   Re(z) gives real parts: 1, 2, 3; Im(z) gives imaginary parts: 1, 2, 3.

2. Step 2: Create named list with real parts as names and imaginary parts as values

   setNames() assigns names to list elements. as.character(Re(z)) converts real parts to strings for names. as.list(Im(z)) converts imaginary parts to list values.

3. Final Answer:

   setNames(as.list(Im(z)), as.character(Re(z))) -> Option D

4. Quick Check:

   Names = real parts, values = imaginary parts [OK]

Hint: Use setNames() with real parts as names, imaginary as values [OK]

Common Mistakes:

• Swapping real and imaginary parts
• Not converting real parts to character for names
• Using list() without names