Complex And Imaginary Numbers Quiz
Complex and imaginary numbers are essential concepts in higher mathematics. Do you think you know everything about the concepts? If yes, then why not give this super awesome quiz a try? All the questions in the quiz are designed to test your knowledge and make you think deeply. Please make sure to read all the questions carefully before answering. We challenge you to get a high score on the quiz, so give this quiz a try! We sincerely wish you all the very best with the quiz.
- 1.
Can you simplify -3i(4 + 2i)?
- A.
120
- B.
-12i - 6i2
- C.
5
- D.
6 - 12i
Correct Answer
D. 6 - 12iExplanation
The expression -3i(4 + 2i) can be simplified by distributing the -3i to both terms inside the parentheses. This results in -12i - 6i^2. Since i^2 is equal to -1, the expression simplifies further to -12i - 6(-1), which becomes -12i + 6. Finally, combining like terms, the simplified expression is 6 - 12i.Rate this question:
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- 2.
Can you simplify it √-25?
- A.
5i
- B.
55i
- C.
100
- D.
None of the above
Correct Answer
A. 5iExplanation
The expression √-25 can be simplified as 5i. This is because the square root of -25 is equal to the square root of 25 multiplied by the square root of -1. The square root of 25 is 5, and the square root of -1 is represented by the imaginary unit i. Therefore, the simplified form of √-25 is 5i.Rate this question:
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- 3.
Can you find the sum (5-2i) + (-7+8i)?
- A.
22+5I
- B.
-2+6i
- C.
55
- D.
100i
Correct Answer
B. -2+6iExplanation
The given question asks for the sum of two complex numbers, (5-2i) and (-7+8i). To find the sum, we simply add the real parts and the imaginary parts separately. Adding the real parts, 5 and -7, we get -2. Adding the imaginary parts, -2i and 8i, we get 6i. Therefore, the sum of (5-2i) and (-7+8i) is -2+6i.Rate this question:
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- 4.
Can you find the solution -4i + 7i?
- A.
-11i
- B.
7i
- C.
3i
- D.
None of the above
Correct Answer
C. 3iExplanation
The solution to -4i + 7i can be found by combining the real and imaginary parts separately. The real part of -4i is 0, and the real part of 7i is also 0. Therefore, the real part of the sum is 0. The imaginary part of -4i is -4, and the imaginary part of 7i is 7. Therefore, the imaginary part of the sum is 7 - 4 = 3. Thus, the correct answer is 3i.Rate this question:
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- 5.
Can you simplify (-3-i)(6-i)?
- A.
-19-3i
- B.
22i
- C.
22i-17i
- D.
None of the above
Correct Answer
A. -19-3iExplanation
To simplify the expression (-3-i)(6-i), we can use the FOIL method. First, we multiply the first terms: -3 * 6 = -18. Then, we multiply the outer terms: -3 * -i = 3i. Next, we multiply the inner terms: -i * 6 = -6i. Finally, we multiply the last terms: -i * -i = i^2 = -1. Combining all these results, we get -18 + 3i - 6i - 1. Simplifying further, we have -19 - 3i.Rate this question:
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- 6.
Can you solve it (Multiply) (4 – 3i)(-7 – 2i)?
- A.
-23 + 13i
- B.
22i
- C.
-34 + 13i
- D.
None of the above
Correct Answer
C. -34 + 13iExplanation
To solve the given multiplication, we can use the FOIL method. Multiplying the first terms of each binomial gives us (4)(-7) = -28. Multiplying the outer terms gives us (4)(-2i) = -8i. Multiplying the inner terms gives us (-3i)(-7) = 21i. Multiplying the last terms gives us (-3i)(-2i) = 6i^2. Simplifying, we have -28 - 8i + 21i + 6i^2. Since i^2 is equal to -1, we can substitute it in the expression to get -28 - 8i + 21i + 6(-1). Combining like terms, we have -28 + 13i - 6, which simplifies to -34 + 13i. Therefore, the correct answer is -34 + 13i.Rate this question:
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- 7.
Can you solve it √-100?
- A.
10i
- B.
100i
- C.
50i
- D.
None of the above
Correct Answer
A. 10iExplanation
The square root of -100 is equal to 10i. In complex numbers, the imaginary unit i is defined as the square root of -1. Therefore, the square root of -100 can be written as 10 * sqrt(-1), which simplifies to 10i.Rate this question:
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- 8.
Can you solve √-81?
- A.
-9i
- B.
99i
- C.
9i
- D.
None of the above
Correct Answer
C. 9iExplanation
The square root of a negative number is an imaginary number. In this case, the square root of -81 is 9i, where i represents the imaginary unit.Rate this question:
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- 9.
Can you find the product of (1+3i)(2-i)?
- A.
34i
- B.
3-2i
- C.
55i
- D.
5+5i
Correct Answer
D. 5+5iExplanation
The product of (1+3i)(2-i) can be found by using the distributive property. First, multiply 1 by 2 and get 2. Then, multiply 1 by -i and get -i. Next, multiply 3i by 2 and get 6i. Finally, multiply 3i by -i and get -3i^2. Simplifying further, -3i^2 can be written as -3(-1), which is equal to 3. Combining all the terms, we get 2 + (-i) + 6i + 3, which simplifies to 5 + 5i. Therefore, the correct answer is 5 + 5i.Rate this question:
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- 10.
What's the basic format for writing the complex number?
- A.
A+bi
- B.
A-bi
- C.
Ai+b
- D.
None of the above
Correct Answer
A. A+biExplanation
The basic format for writing a complex number is a+bi, where 'a' represents the real part of the number and 'b' represents the imaginary part. The imaginary part is multiplied by 'i', the imaginary unit. This format allows us to represent numbers that have both a real and imaginary component, such as 3+2i, where 3 is the real part and 2i is the imaginary part. The other options provided, a-bi and ai+b, do not follow the standard format for writing complex numbers.Rate this question:
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Current Version
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Aug 16, 2023Quiz Edited by
ProProfs Editorial Team -
Nov 10, 2022Quiz Created by
Tanya Mishra
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