Calculate $$(3 - 6i)^2$$ .

$$(3 - 6i)^2 = 9 - 36i + 36i^2 = 9 - 36i - 36 = -27 - 36i$$ .

What is the result of $$(3 - 2i)(7 + 6i)$$ ?

$$(3 - 2i)(7 + 6i) = 21 + 18i - 14i - 12i^2 = 21 + 4i + 12 = 33 + 4i$$ .

Calculate $$(5 + 6i)(1 - 7i)$$ .

$$(5 + 6i)(1 - 7i) = 5 - 35i + 6i - 42i^2 = 5 - 29i + 42 = 47 - 29i$$ .

What is the product of $$(4 + 3i)(2 + 2i)$$ ?

$$(4 + 3i)(2 + 2i) = 8 + 8i + 6i + 6i^2 = 8 + 14i - 6 = 2 + 14i$$ .

Calculate $$i(2i)(8i)$$ .

$$i(2i)(8i) = i(16i^2) = i(-16) = -16i$$ .

What is the imaginary unit $$i$$ ?

The imaginary unit $$i$$ is defined as $$i = \text{sqrt}(-1)$$ , and it satisfies the property $$i^2 = -1$$ .

Explain the concept of conjugate of a complex number.

The conjugate of a complex number $$a + bi$$ is $$a - bi$$ . It is used in division and simplifying expressions involving complex numbers.

What is the modulus of a complex number?

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

How do you add two complex numbers?

To add two complex numbers $$(a + bi) + (c + di)$$ , simply add the real parts and the imaginary parts: $$(a + c) + (b + d)i$$ .

What is the geometric representation of complex numbers?

Complex numbers can be represented on the complex plane, where the x-axis represents the real part and the y-axis represents the imaginary part.

What is the difference between real and imaginary parts of a complex number?

In a complex number $$a + bi$$ , $$a$$ is the real part and $$b$$ is the imaginary part. The real part is a number on the real number line, while the imaginary part is a multiple of $$i$$ .

How do you subtract two complex numbers?

To subtract two complex numbers $$(a + bi) - (c + di)$$ , subtract the real parts and the imaginary parts: $$(a - c) + (b - d)i$$ .

Multiplying Complex Numbers

Flashcard

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Mathematics

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11th Grade

•

Practice Problem

•

Hard

•

CCSS

HSN.CN.A.2, HSN.CN.A.1, HSN.CN.C.8

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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

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What is the formula for multiplying two complex numbers?

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CCSS.HSN.CN.A.2

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CCSS.HSN.CN.C.8

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CCSS.HSN.CN.C.8

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CCSS.HSN.CN.A.2

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CCSS.HSN.CN.A.2

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CCSS.HSN.CN.A.2

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