adding subtracting multiplying and dividing complex numbers

Flashcard
•
Mathematics
•
10th - 12th Grade
•
Hard
+1
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 i = √(-1).
Tags
CCSS.HSN.CN.A.1
2.
FLASHCARD QUESTION
Front
How do you add complex numbers?
Back
To add complex numbers, combine the real parts and the imaginary parts separately. For example, (a + bi) + (c + di) = (a + c) + (b + d)i.
Tags
CCSS.HSN.CN.A.2
3.
FLASHCARD QUESTION
Front
How do you subtract complex numbers?
Back
To subtract complex numbers, subtract the real parts and the imaginary parts separately. For example, (a + bi) - (c + di) = (a - c) + (b - d)i.
Tags
CCSS.HSN.CN.A.2
4.
FLASHCARD QUESTION
Front
What is the product of two complex numbers?
Back
The product of two complex numbers (a + bi)(c + di) is calculated using the distributive property: ac + adi + bci + bdi^2, which simplifies to (ac - bd) + (ad + bc)i.
Tags
CCSS.HSN.CN.A.2
5.
FLASHCARD QUESTION
Front
How do you divide complex numbers?
Back
To divide 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) to eliminate the imaginary part in the denominator.
Tags
CCSS.HSN.CN.A.3
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 used in division to eliminate the imaginary part from the denominator.
Tags
CCSS.HSN.CN.A.3
7.
FLASHCARD QUESTION
Front
What is the imaginary unit 'i'?
Back
The imaginary unit 'i' is defined as the square root of -1, i.e., i = √(-1). It is used to extend the real number system to complex numbers.
Tags
CCSS.HSN.CN.A.1
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