Complex type in R Programming - 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.

R Programming

z <- complex(real = [1], imaginary = 4)

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

A4

B3

C5

D0

Attempts:

3 left

💡 Hint

Common Mistakes

Putting the imaginary part in the real argument.

Using 0 instead of 3 for the real part.

The complex() function creates a complex number. The real part is 3, so we fill in 3.

2fill in blank

medium

Complete the code to get the imaginary part of the complex number z.

R Programming

imag_part <- [1](z)

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AMod

BRe

CArg

DIm

Attempts:

3 left

💡 Hint

Common Mistakes

Using Re() which returns the real part.

Using Mod() which returns the magnitude.

The function Im() returns the imaginary part of a complex number in R.

3fill in blank

hard

Fix the error in the code to create a complex number with real part 2 and imaginary part 5.

R Programming

z <- complex([1] = 2, imaginary = 5)

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Aimaginary

Bimag

Creal

Dim

Attempts:

3 left

💡 Hint

Common Mistakes

Using imaginary for the real part.

Using incorrect argument names like im or imag.

The correct argument name for the real part in complex() is real.

4fill in blank

hard

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

R Programming

z_vec <- complex(real = [1], imaginary = [2])

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A1:3

B4:6

Cc(1,2,3)

Dc(4,5,6)

Attempts:

3 left

💡 Hint

Common Mistakes

Using mismatched lengths for real and imaginary parts.

Using vectors with wrong values.

Use 1:3 for real parts and 4:6 for imaginary parts to create the vector.

5fill in blank

hard

Fill all three blanks to create a named list of complex numbers where keys are uppercase letters and values are complex numbers with real parts 1 to 3 and imaginary parts 3 to 5.

R Programming

names <- toupper(letters[1:3])
values <- complex(real = [1], imaginary = [2])
complex_list <- setNames([3], names)

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A1:3

B3:5

Cvalues

Dc(1,2,3)

Attempts:

3 left

💡 Hint

Common Mistakes

Using wrong sequences for real or imaginary parts.

Putting the wrong variable inside the list.

Use 1:3 for real parts, 3:5 for imaginary parts, and the variable values as the list elements.

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