Operations with Complex Numbers

Flashcard
•
Mathematics
•
10th - 12th Grade
•
Hard
+1
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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.
Tags
CCSS.HSN.CN.A.1
2.
FLASHCARD QUESTION
Front
What is the imaginary unit 'i'?
Back
The imaginary unit 'i' is defined as i = √(-1). It is used to represent the square root of negative numbers.
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 (a + bi)(c + di)?
Back
The product is given by (a + bi)(c + di) = ac + adi + bci + bdi². Since i² = -1, it simplifies to (ac - bd) + (ad + bc)i.
Tags
CCSS.HSN.CN.A.2
6.
FLASHCARD QUESTION
Front
What is the conjugate of a complex number a + bi?
Back
The conjugate of a complex number a + bi is a - bi. It is obtained by changing the sign of the imaginary part.
Tags
CCSS.HSN.CN.A.3
7.
FLASHCARD QUESTION
Front
How do you multiply a complex number by its conjugate?
Back
Multiplying a complex number by its conjugate results in a real number: (a + bi)(a - bi) = a² + b².
Tags
CCSS.HSN.CN.C.8
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