What is the conjugate of a complex number?

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

How do you divide two complex numbers?

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

What is the modulus of a complex number?

The modulus of a complex number $$a + bi$$ is given by $$|a + bi| = \text{sqrt}(a^2 + b^2)$$ . It represents the distance from the origin in the complex plane.

What is the argument of a complex number?

The argument of a complex number $$a + bi$$ is the angle $$\theta$$ formed with the positive real axis, calculated as $$\theta = \text{tan}^{-1}(\frac{b}{a})$$ .

What is the polar form of a complex number?

The polar form of a complex number is expressed as $$r(\text{cos}(\theta) + i\text{sin}(\theta))$$ , where $$r$$ is the modulus and $$\theta$$ is the argument.

Complex Number Operations and 'i' Flashcards

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1.

FLASHCARD QUESTION

Front

Define a complex number.

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CCSS.HSN.CN.A.1

2.

FLASHCARD QUESTION

Front

What is the imaginary unit 'i'?

Back

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CCSS.HSN.CN.A.1

3.

FLASHCARD QUESTION

Front

How do you add two complex numbers?

Back

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CCSS.HSN.CN.A.2

4.

FLASHCARD QUESTION

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How do you subtract two complex numbers?

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CCSS.HSN.CN.A.2

5.

FLASHCARD QUESTION

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What is the formula for multiplying two complex numbers?

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CCSS.HSN.CN.A.2

6.

FLASHCARD QUESTION

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CCSS.HSN.CN.A.2

7.

FLASHCARD QUESTION

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CCSS.HSN.CN.C.8

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