What is the modulus of a complex number?

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

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.

What is the exponential form of a complex number?

The exponential form of a complex number is expressed as $$re^{i\theta}$$ , where $$r$$ is the modulus and $$\theta$$ is the argument.

How do you simplify $$ \text{sqrt}(-x) $$ ?

$$\text{sqrt}(-x) = \text{sqrt}(x)i$$ .

What is the value of $$i^{21}$$ ?

$$i^{21} = i$$ , since the powers of $$i$$ cycle every four: $$i, -1, -i, 1$$ .

What is the result of $$ (1 + 3i) + (7 - 2i) $$ ?

$$ (1 + 3i) + (7 - 2i) = 8 + i $$ .

What is the simplified form of $$ \frac{4 - 4i}{9 + 5i} $$ ?

$$ \frac{4 - 4i}{9 + 5i} = \frac{8}{53} - \frac{28}{53}i $$ .

Complex Number Operations Flashcards

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1.

FLASHCARD QUESTION

Front

What is a complex number?

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2.

FLASHCARD QUESTION

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3.

FLASHCARD QUESTION

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How do you add complex numbers?

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4.

FLASHCARD QUESTION

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How do you subtract complex numbers?

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5.

FLASHCARD QUESTION

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What is the product of two complex numbers?

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6.

FLASHCARD QUESTION

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What is the conjugate of a complex number?

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7.

FLASHCARD QUESTION

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How do you divide complex numbers?

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