Complex Numbers 1

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•
Mathematics
•
11th Grade
•
Hard
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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 complex numbers.
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.
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.
5.
FLASHCARD QUESTION
Front
What is the complex conjugate of a complex number?
Back
The complex 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
What is the modulus of a complex number?
Back
The modulus of a complex number a + bi is given by |a + bi| = √(a² + b²). It represents the distance of the point (a, b) from the origin in the complex plane.
7.
FLASHCARD QUESTION
Front
How do you multiply complex numbers?
Back
To multiply complex numbers, use the distributive property: (a + bi)(c + di) = ac + adi + bci + bdi². Remember that i² = -1.
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