Dividing Complex Numbers with conjugates

Flashcard
•
Mathematics
•
11th - 12th Grade
•
Hard
+2
Standards-aligned
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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.
Tags
CCSS.HSN.CN.A.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 obtained by changing the sign of the imaginary part.
Tags
CCSS.HSN.CN.A.3
3.
FLASHCARD QUESTION
Front
Why do we multiply by the conjugate when dividing complex numbers?
Back
Multiplying by the conjugate helps eliminate the imaginary part from the denominator, making it a real number.
Tags
CCSS.HSN.CN.A.3
4.
FLASHCARD QUESTION
Front
What is the formula for multiplying two complex numbers?
Back
If z1 = a + bi and z2 = c + di, then z1 * z2 = (ac - bd) + (ad + bc)i.
Tags
CCSS.HSN.CN.A.2
5.
FLASHCARD QUESTION
Front
How do you simplify a complex fraction?
Back
To simplify a complex fraction, multiply the numerator and denominator by the conjugate of the denominator.
6.
FLASHCARD QUESTION
Front
What is the result of multiplying (2 + 3i) by its conjugate?
Back
The result is 2^2 + 3^2 = 4 + 9 = 13.
Tags
CCSS.HSN.CN.C.8
7.
FLASHCARD QUESTION
Front
What is the denominator after multiplying (1 + 2i) by its conjugate (1 - 2i)?
Back
The denominator is 1^2 + (2)^2 = 1 + 4 = 5.
Tags
CCSS.HSN.CN.A.3
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