What is the imaginary unit $$i$$ ?

The imaginary unit $$i$$ is defined as $$i = \text{sqrt}(-1)$$ . It is used to extend the real number system to include solutions to equations that do not have real solutions.

What is the square root of a negative number, such as $$-36$$ ?

The square root of $$-36$$ is $$6i$$ .

What is the modulus of a complex number $$a + bi$$ ?

The modulus of a complex number is given by $$|z| = \text{sqrt}(a^2 + b^2)$$ .

What is the argument of a complex number $$a + bi$$ ?

The argument of a complex number 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 Numbers: Operations

Complex numbers: Operations

Flashcard

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Mathematics

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10th Grade

•

Practice Problem

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Hard

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CCSS

HSN.CN.A.3, HSN.CN.A.2, HSN.CN.A.1

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FLASHCARD QUESTION

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Define a complex number.

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CCSS.HSN.CN.A.1

FLASHCARD QUESTION

Front

Back

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CCSS.HSN.CN.A.1

FLASHCARD QUESTION

Front

How do you add two complex numbers?

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CCSS.HSN.CN.A.2

FLASHCARD QUESTION

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How do you subtract two complex numbers?

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CCSS.HSN.CN.A.2

FLASHCARD QUESTION

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What is the product of two complex numbers?

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CCSS.HSN.CN.A.2

FLASHCARD QUESTION

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How do you divide complex numbers?

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CCSS.HSN.CN.A.3

FLASHCARD QUESTION

Front

What is the conjugate of a complex number?

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CCSS.HSN.CN.A.3

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