adding subtracting multiplying and dividing complex numbers

Flashcard
•
Mathematics
•
10th - 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
How do you add two complex numbers?
Back
To add two complex numbers, you add their real parts and their imaginary parts separately. For example, (a + bi) + (c + di) = (a + c) + (b + d)i.
3.
FLASHCARD QUESTION
Front
How do you subtract two complex numbers?
Back
To subtract two complex numbers, you subtract their real parts and their imaginary parts separately. For example, (a + bi) - (c + di) = (a - c) + (b - d)i.
4.
FLASHCARD QUESTION
Front
What is the product of two complex numbers?
Back
The product of two complex numbers (a + bi) and (c + di) is given by (ac - bd) + (ad + bc)i.
5.
FLASHCARD QUESTION
Front
How do you divide two complex numbers?
Back
To divide two 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).
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 obtained by changing the sign of the imaginary part.
7.
FLASHCARD QUESTION
Front
What is the modulus of a complex number?
Back
The modulus of a complex number a + bi is given by √(a² + b²). It represents the distance of the complex number from the origin in the complex plane.
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