What is a complex number?
Complex Number Calculations

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•
Mathematics
•
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
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.
3.
FLASHCARD QUESTION
Front
What is the result of adding (-7 + 6i) and (3 + 2i)?
Back
-4 + 8i.
4.
FLASHCARD QUESTION
Front
How do you multiply complex numbers?
Back
To multiply complex numbers, use the distributive property (FOIL method) and apply the fact that i^2 = -1. For example, (a + bi)(c + di) = ac + adi + bci + bdi^2.
5.
FLASHCARD QUESTION
Front
What is the result of multiplying (-1 + 2i) and (-2 - 3i)?
Back
8 - 1i.
6.
FLASHCARD QUESTION
Front
What is the imaginary unit 'i'?
Back
The imaginary unit 'i' is defined as the square root of -1, which means i^2 = -1.
7.
FLASHCARD QUESTION
Front
What happens when you multiply two imaginary numbers?
Back
When you multiply two imaginary numbers, the result is a real number. For example, (ai)(bi) = ab(i^2) = -ab.
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