What is a complex number?
Dividing Complex Numbers

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•
Mathematics
•
11th - 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^2 = -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 used in division to eliminate the imaginary part from the denominator.
3.
FLASHCARD QUESTION
Front
How do you multiply complex numbers?
Back
To multiply complex numbers (a + bi)(c + di), use the distributive property: ac + adi + bci + bdi^2, and simplify using i^2 = -1.
4.
FLASHCARD QUESTION
Front
What is the formula for dividing complex numbers?
Back
To divide complex numbers \( \frac{a + bi}{c + di} \), multiply the numerator and denominator by the conjugate of the denominator: \( \frac{(a + bi)(c - di)}{(c + di)(c - di)} \).
5.
FLASHCARD QUESTION
Front
Simplify \( \frac{8 + 5i}{1 - 7i} \).
Back
\( \frac{-27 + 61i}{50} \)
6.
FLASHCARD QUESTION
Front
Simplify \( \frac{12}{8i} \).
Back
\( -\frac{3i}{2} \)
7.
FLASHCARD QUESTION
Front
Simplify \( \frac{14}{7 - 6i} \).
Back
\( \frac{98 + 84i}{85} \)
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