Which one of the below is right about z-z*?

Always purely imaginary or zero

Pre-calculus | Topic: Complex Roots | Level One: Complex Numbers

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| By Johnalzate

Johnalzate

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Quizzes Created: 2 | Total Attempts: 774

Questions: 12 | Attempts: 90 | Updated: Jul 27, 2023

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Pre-calculus | Topic: Complex Roots | Level One: Complex Numbers - Quiz

Welcome to your Level One review quiz on Complex Numbers. The following quiz will test you on basic properties of i.
REMEMBER
Standard form for complex number: a + bi

Questions and Answers

1.

Port 20 is for the "___" and works with port "___" for the Control.
- A.
  
  "Triggering" "22"
- B.
  
  "Data" "21"
- C.
  
  "Access" "21"
- D.
  
  "SSH" "22"
Correct Answer
B. "Data" "21"

Explanation
Port 20 is used for the "Data" transfer in FTP (File Transfer Protocol) and it works in conjunction with port "21" which is used for the control commands.

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2.

SSH is asigned to what port number?
- A.
  
  21
- B.
  
  22
- C.
  
  23
- D.
  
  23 and 24
Correct Answer
B. 22

Explanation
SSH (Secure Shell) is a network protocol that allows secure remote access to a computer or server. It is commonly used for secure remote administration and file transfers. The correct answer is 22 because SSH is typically assigned to port number 22.

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3.

TFTP stands for:
- A.
  
  Trigger Flash Telnet Protection
- B.
  
  Tunnel Filing Translation Protocol
- C.
  
  Trivial File Transfer Protocol
- D.
  
  The Fun Time Party
Correct Answer
C. Trivial File Transfer Protocol

Explanation
TFTP stands for Trivial File Transfer Protocol. It is a simple and lightweight file transfer protocol that is commonly used for transferring files between network devices. Unlike other file transfer protocols, TFTP does not have features like authentication or directory listing, making it less secure but faster and easier to implement. TFTP is often used in scenarios where speed and simplicity are more important than security, such as booting diskless workstations or transferring firmware updates to network devices.

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4.

TFTP is assigned to which port?
- A.
  
  69
- B.
  
  72
- C.
  
  73 and 75
- D.
  
  No assigned port
Correct Answer
A. 69

Explanation
TFTP (Trivial File Transfer Protocol) is assigned to port number 69. This port is used for transferring files between a client and a server in a simple and lightweight manner. TFTP is commonly used for network booting, firmware updates, and other similar operations where a small and fast file transfer protocol is needed.

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5.

DHCP uses which TWO ports?
- A.
  
  65
- B.
  
  66
- C.
  
  67
- D.
  
  68
- E.
  
  69
Correct Answer(s)
C. 67
D. 68

Explanation
DHCP (Dynamic Host Configuration Protocol) uses port numbers 67 and 68. Port 67 is used by DHCP servers to receive client requests and provide IP configuration information, while port 68 is used by DHCP clients to send requests and receive IP configuration from DHCP servers. These port numbers are standardized and widely used for DHCP communication.

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6.

In the list below, which choice has both of the Mail Recieving Protocols with their proper assigned port numbers? (READ THE WHOLE ANSWER!)
- A.
  
  SMTP: 25, IMAP: 143
- B.
  
  IMAP: 134, POP3: 110
- C.
  
  SMTP: 25, POP3: 110
- D.
  
  HTTPS: 443, SMTP: 25
- E.
  
  IMAP: 143, POP3, 110
Correct Answer
E. IMAP: 143, POP3, 110

Explanation
The correct answer is "IMAP: 143, POP3: 110". This choice includes both of the Mail Receiving Protocols (IMAP and POP3) with their proper assigned port numbers (IMAP: 143, POP3: 110).

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7.

If z is real, what is z*?
- A.
  
  A real number
- B.
  
  A complex number
- C.
  
  A purely imaginary number
- D.
  
  Zero
Correct Answer
A. A real number

Explanation
The complex conjugate of a real number is itself, so if z is real, then z* will also be a real number.

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8.

Which one of the below is right about z-z*?
- A.
  
  Always purely imaginary or zero
- B.
  
  Always real number
- C.
  
  Always zero
- D.
  
  Always purely imaginary
Correct Answer
A. Always purely imaginary or zero

Explanation
The expression z-z* represents the difference between a complex number z and its complex conjugate z*. The complex conjugate of a complex number has the same real part but the imaginary part with opposite sign. Therefore, when we subtract z* from z, the real parts cancel out, leaving only the imaginary part. This means that z-z* is always purely imaginary or zero.

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9.

Given that (a+i)(3+bi)=40-74i find the values of a and b where a and b are integers.
- A.
  
  A=11, b=7
- B.
  
  A=11, b= - 7
- C.
  
  A= - 11, b=7
- D.
  
  A= - 11, b= - 7
Correct Answer
C. A= - 11, b=7

Explanation
The given equation is a complex number equation in the form (a+i)(3+bi)=40-74i. By multiplying the terms using the FOIL method, we get 3a + 3bi + ai - b = 40 - 74i. Equating the real and imaginary parts of the equation separately, we get 3a - b = 40 and 3b + a = -74. Solving these two equations simultaneously, we find that a = -11 and b = 7, which matches the given answer.

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10.

If z=1+2i and w=3-i, find which one of the follow represents z+w?
- A.
  
  Option 1
- B.
  
  Option 2
- C.
  
  Option 3
- D.
  
  Option 4
Correct Answer
B. Option 2

Explanation
The correct answer is Option 2 because to find z+w, we need to add the real parts and the imaginary parts separately. The real part of z is 1 and the real part of w is 3, so the real part of z+w is 1+3=4. The imaginary part of z is 2i and the imaginary part of w is -i, so the imaginary part of z+w is 2i+(-i)=i. Therefore, z+w is equal to 4+i, which is represented by Option 2.

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11.

If z=1+2i and w=3-i, find which one of the follow represents w-3z?
- A.
  
  Option 1
- B.
  
  Option 2
- C.
  
  Option 3
- D.
  
  Option 4
Correct Answer
D. Option 4

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Current Version
Jul 27, 2023

Quiz Edited by
ProProfs Editorial Team
Nov 15, 2011

Quiz Created by
Johnalzate

Pre-calculus | Topic: Complex Roots | Level One: Complex Numbers

Port 20 is for the "___" and works with port "___" for the Control.

SSH is asigned to what port number?

TFTP stands for:

TFTP is assigned to which port?

DHCP uses which TWO ports?

In the list below, which choice has both of the Mail Recieving Protocols with their proper assigned port numbers? (READ THE WHOLE ANSWER!)

If z is real, what is z*?

Which one of the below is right about z-z*?

Given that (a+i)(3+bi)=40-74i find the values of a and b where a and b are integers.

If z=1+2i and w=3-i, find which one of the follow represents z+w?

If z=1+2i and w=3-i, find which one of the follow represents w-3z?

Port 20 is for the "_" and works with port "_" for the Control.