How do you simplify the square root of a negative number?

To simplify the square root of a negative number, factor out $$-1$$ : For example, $$\text{sqrt}(-x) = i\text{sqrt}(x)$$ .

What is the formula for multiplying complex numbers in polar form?

To multiply complex numbers in polar form, multiply their magnitudes and add their angles: If $$z_1 = r_1(\text{cos}(\theta_1) + i\text{sin}(\theta_1))$$ and $$z_2 = r_2(\text{cos}(\theta_2) + i\text{sin}(\theta_2))$$ , then $$z_1z_2 = r_1r_2(\text{cos}(\theta_1 + \theta_2) + i\text{sin}(\theta_1 + \theta_2))$$ .

What is the conjugate of a complex number?

The conjugate of a complex number $$a + bi$$ is $$a - bi$$ . It is used to simplify division of complex numbers.

How do you divide complex numbers?

To divide complex numbers, multiply the numerator and denominator by the conjugate of the denominator. For example, to divide $$\frac{a + bi}{c + di}$$ , multiply by $$\frac{c - di}{c - di}$$ .

What is the geometric interpretation of complex numbers?

Complex numbers can be represented as points or vectors in a 2D plane, known as the complex plane, where the x-axis represents the real part and the y-axis represents the imaginary part.

Complex Number Operations and 'i' Flashcards

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16 questions

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1.

FLASHCARD QUESTION

Front

Define a complex number.

Back

Tags

CCSS.HSN.CN.A.1

2.

FLASHCARD QUESTION

Front

What is the imaginary unit 'i'?

Back

Tags

CCSS.HSN.CN.A.1

3.

FLASHCARD QUESTION

Front

How do you multiply two complex numbers?

Back

Tags

CCSS.HSN.CN.A.2

4.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSN.CN.A.2

5.

FLASHCARD QUESTION

Front

What is the formula for adding complex numbers?

Back

Tags

CCSS.HSN.CN.A.2

6.

FLASHCARD QUESTION

Front

What is the formula for subtracting complex numbers?

Back

Tags

CCSS.HSN.CN.A.2

7.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSN.CN.C.8

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