What is the result of multiplying $$(3 - i)(4 + 5i)$$ ?

The result is $$(3 - i)(4 + 5i) = 12 + 15i - 4i - 5 = 7 + 11i$$ .

How do you simplify $$(2 + 3i)(-1 + 6i)$$ ?

To simplify, use the distributive property: $$(2)(-1) + (2)(6i) + (3i)(-1) + (3i)(6i) = -2 + 12i - 3i + 18(-1) = -2 + 9i - 18 = -20 + 9i$$ .

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 $$\theta = \tan^{-1}(\frac{b}{a})$$ .

What is the standard form of a complex number?

The standard form of a complex number is $$a + bi$$ , where $$a$$ is the real part and $$b$$ is the imaginary part.

What is the real part of the complex number $$5 + 3i$$ ?

The real part of the complex number $$5 + 3i$$ is $$5$$ .

What is the imaginary part of the complex number $$5 + 3i$$ ?

The imaginary part of the complex number $$5 + 3i$$ is $$3$$ .

How do you add two complex numbers?

To add two complex numbers, simply add their real parts and their imaginary parts separately. For example, $$(a + bi) + (c + di) = (a + c) + (b + d)i$$ .

How do you subtract two complex numbers?

To subtract two complex numbers, subtract their real parts and their imaginary parts separately. For example, $$(a + bi) - (c + di) = (a - c) + (b - d)i$$ .

What is the result of multiplying $$(3 + i)(3 - i)$$ ?

The result is $$(3 + i)(3 - i) = 9 - i^2 = 9 - (-1) = 10$$ .

What is the significance of the conjugate in division of complex numbers?

The conjugate is used to eliminate the imaginary part in the denominator when dividing complex numbers. For example, to divide $$\frac{a + bi}{c + di}$$ , multiply the numerator and denominator by the conjugate of the denominator.

Multiplying Complex Numbers

Flashcard

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Mathematics

•

10th - 12th Grade

•

Practice Problem

•

Hard

•

CCSS

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

Standards-aligned

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FLASHCARD QUESTION

Front

What is a complex number?

Back

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CCSS.HSN.CN.A.1

FLASHCARD QUESTION

Front

What is the imaginary unit?

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CCSS.HSN.CN.A.1

FLASHCARD QUESTION

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How do you multiply two complex numbers?

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CCSS.HSN.CN.A.2

FLASHCARD QUESTION

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CCSS.HSN.CN.A.2

FLASHCARD QUESTION

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What is the conjugate of a complex number?

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CCSS.HSN.CN.A.3

FLASHCARD QUESTION

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Back

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CCSS.HSN.CN.A.2

FLASHCARD QUESTION

Front

What is the modulus of a complex number?

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