Complex Numbers 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 the square root of -1.
2.
FLASHCARD QUESTION
Front
What is the imaginary unit 'i'?
Back
The imaginary unit 'i' is defined as the square root of -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
How do you add complex numbers?
Back
To add complex numbers, combine the real parts and the imaginary parts separately. For example, (a + bi) + (c + di) = (a + c) + (b + d)i.
4.
FLASHCARD QUESTION
Front
How do you subtract complex numbers?
Back
To subtract complex numbers, subtract the real parts and the imaginary parts separately. For example, (a + bi) - (c + di) = (a - c) + (b - d)i.
5.
FLASHCARD QUESTION
Front
What is the conjugate of a complex number?
Back
The conjugate of a complex number a + bi is a - bi. It is obtained by changing the sign of the imaginary part.
6.
FLASHCARD QUESTION
Front
How do you multiply complex numbers?
Back
To multiply complex numbers, use the distributive property (FOIL). For example, (a + bi)(c + di) = ac + adi + bci + bdi^2, and since i^2 = -1, combine like terms.
7.
FLASHCARD QUESTION
Front
What is the modulus of a complex number?
Back
The modulus of a complex number a + bi is the distance from the origin to the point (a, b) in the complex plane, calculated as |a + bi| = √(a² + b²).
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