complex numbers 1st sem final review

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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 imaginary unit 'i'?
Back
The imaginary unit 'i' is defined as 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
What is the conjugate of a complex number a + bi?
Back
The conjugate of a complex number a + bi is a - bi.
4.
FLASHCARD QUESTION
Front
How do you add two complex numbers?
Back
To add two complex numbers, add their real parts and their imaginary parts separately. For example, (a + bi) + (c + di) = (a + c) + (b + d)i.
5.
FLASHCARD QUESTION
Front
How do you subtract two complex numbers?
Back
To subtract two complex numbers, subtract their real parts and their imaginary parts separately. For example, (a + bi) - (c + di) = (a - c) + (b - d)i.
6.
FLASHCARD QUESTION
Front
What is the product of two complex numbers (a + bi)(c + di)?
Back
The product is given by (ac - bd) + (ad + bc)i.
7.
FLASHCARD QUESTION
Front
What is the simplified form of (8 - 3i)²?
Back
The simplified form is 55 - 48i.
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