Complex type in R Programming - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is a complex type in R?

A complex type in R is a data type used to store numbers with both real and imaginary parts, like 3 + 2i.

beginner

How do you create a complex number in R?

You can create a complex number by using the syntax: complex(real = 3, imaginary = 2) or simply by writing 3 + 2i.

beginner

What function returns the imaginary part of a complex number in R?

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

intermediate

What does the Mod() function do with a complex number in R?

The Mod() function returns the modulus (or absolute value) of a complex number, which is the distance from zero in the complex plane.

beginner

How can you add two complex numbers in R?

You add two complex numbers just like regular numbers using the + operator, for example: (3 + 2i) + (1 + 4i).

Which of the following is a valid complex number in R?

A 5 + 3

B 5 + 3j

C 5i + 3

D 5 + 3i

In R, complex numbers use 'i' for the imaginary part, so '5 + 3i' is correct.

What does the function Re() return when used on a complex number?

A Imaginary part

B Argument

C Real part

D Modulus

Re() returns the real part of a complex number.

How do you find the argument (angle) of a complex number in R?

A Using <code>Arg()</code>

B Using <code>Mod()</code>

C Using <code>Im()</code>

D Using <code>Re()</code>

Arg() returns the argument (angle) of a complex number.

What is the output of Mod(3 + 4i) in R?

A 5

B 7

C 1

D 12

The modulus is sqrt(3^2 + 4^2) = 5.

Which function creates a complex number from real and imaginary parts in R?

A makeComplex()

B complex()

C complexify()

D createComplex()

The complex() function creates complex numbers from real and imaginary parts.

Explain how to create and use complex numbers in R with examples.

Think about how you write complex numbers and how to get their parts.

Describe the functions used to get the modulus and argument of a complex number in R and why they are useful.

Consider the complex number as a point on a plane.

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