Complex Numbers Practice (Basic)

Flashcard
•
Mathematics
•
9th - 12th Grade
•
Hard
Standards-aligned
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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).
Tags
CCSS.HSN.CN.A.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.
Tags
CCSS.HSN.CN.A.1
3.
FLASHCARD QUESTION
Front
How do you add complex numbers?
Back
To add complex numbers, combine their real parts and their imaginary parts separately. For example, (a + bi) + (c + di) = (a + c) + (b + d)i.
Tags
CCSS.HSN.CN.A.2
4.
FLASHCARD QUESTION
Front
How do you subtract complex numbers?
Back
To subtract complex numbers, subtract their real parts and their imaginary parts separately. For example, (a + bi) - (c + di) = (a - c) + (b - d)i.
Tags
CCSS.HSN.CN.A.2
5.
FLASHCARD QUESTION
Front
What is the product of two complex numbers?
Back
To multiply two complex numbers (a + bi) and (c + di), use the distributive property: (a + bi)(c + di) = ac + adi + bci + bdi^2. Remember that i^2 = -1.
Tags
CCSS.HSN.CN.A.2
6.
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 used in division of complex numbers to eliminate the imaginary part from the denominator.
Tags
CCSS.HSN.CN.A.3
7.
FLASHCARD QUESTION
Front
How do you find the modulus of a complex number?
Back
The modulus of a complex number a + bi is given by |a + bi| = √(a^2 + b^2). It represents the distance of the complex number from the origin in the complex plane.
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