What is a complex number?
Operations on Complex Numbers

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Mathematics
•
9th - 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 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 include solutions to equations that do not have real solutions.
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 product of two complex numbers?
Back
To multiply complex numbers, use the distributive property (FOIL method). For example, (a + bi)(c + di) = ac + adi + bci + bdi^2, and since i^2 = -1, it simplifies to (ac - bd) + (ad + bc)i.
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 and to simplify expressions.
7.
FLASHCARD QUESTION
Front
How do you divide complex numbers?
Back
To divide complex numbers, multiply the numerator and denominator by the conjugate of the denominator. For example, to divide (a + bi) by (c + di), multiply by (c - di)/(c - di).
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