What is a complex number?
Multiply Complex Numbers

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Mathematics
•
10th - 12th Grade
•
Hard
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1.
FLASHCARD QUESTION
Front
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 multiply two complex numbers (a + bi)(c + di)?
Back
To multiply two complex numbers, use the distributive property: (a + bi)(c + di) = ac + adi + bci + bdi^2. Since i^2 = -1, this simplifies to (ac - bd) + (ad + bc)i.
4.
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.
5.
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.
6.
FLASHCARD QUESTION
Front
What is the geometric interpretation of complex numbers?
Back
Complex numbers can be represented as points or vectors in a two-dimensional plane, known as the complex plane, where the x-axis represents the real part and the y-axis represents the imaginary part.
7.
FLASHCARD QUESTION
Front
How do you express a complex number in polar form?
Back
A complex number can be expressed in polar form as r(cos θ + i sin θ), where r is the modulus (magnitude) and θ is the argument (angle) of the complex number.
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