Operations on COmplex Numbers

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•
Mathematics
•
11th - 12th 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 the square root of -1.
2.
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.
3.
FLASHCARD QUESTION
Front
How do you multiply 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.
4.
FLASHCARD QUESTION
Front
What is the result of multiplying (3 + 2i) and (1 - 4i)?
Back
(3 + 2i)(1 - 4i) = 3 - 12i + 2i - 8i^2 = 3 - 10i + 8 = 11 - 10i.
5.
FLASHCARD QUESTION
Front
How do you divide complex numbers?
Back
To divide complex numbers (a + bi) by (c + di), multiply the numerator and denominator by the conjugate of the denominator: (a + bi)/(c + di) * (c - di)/(c - di).
6.
FLASHCARD QUESTION
Front
What is the simplified form of i^2?
Back
i^2 = -1.
7.
FLASHCARD QUESTION
Front
What is the simplified form of √(-1)?
Back
√(-1) = i.
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