Complex Number Practice

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•
Mathematics
•
9th - 12th Grade
•
Hard
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15 questions
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1.
FLASHCARD QUESTION
Front
What is a complex number?
Back
A complex number is a number that can be expressed in the form a + bi, where a and b are real numbers, and i is the imaginary unit, defined as i = √(-1).
2.
FLASHCARD QUESTION
Front
What is the imaginary unit 'i'?
Back
The imaginary unit 'i' is defined as the square root of -1, i.e., i = √(-1). It is used to extend the real number system to include solutions to equations that do not have real solutions.
3.
FLASHCARD QUESTION
Front
What is the complex conjugate of a complex number a + bi?
Back
The complex conjugate of a complex number a + bi is a - bi. It is obtained by changing the sign of the imaginary part.
4.
FLASHCARD QUESTION
Front
What is the product of a complex number and its conjugate?
Back
The product of a complex number a + bi and its conjugate a - bi is a^2 + b^2.
5.
FLASHCARD QUESTION
Front
How do you simplify the square root of a negative number, such as √-k?
Back
To simplify √-k, you can express it as i√k, where k is a positive real number.
6.
FLASHCARD QUESTION
Front
What is the simplified form of (a + bi)^2?
Back
The simplified form of (a + bi)^2 is a^2 - b^2 + 2abi.
7.
FLASHCARD QUESTION
Front
What is the sum of two complex numbers (a + bi) and (c + di)?
Back
The sum of two complex numbers (a + bi) and (c + di) is (a + c) + (b + d)i.
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