What is the product of two complex numbers $$(a + bi)(c + di)$$ ?

The product is given by $$(ac - bd) + (ad + bc)i$$ .

Simplify the expression $$(2 + 3i)(-1 + 6i)$$ .

The simplified form is $$-20 + 9i$$ .

What is the imaginary unit $$i$$ ?

The imaginary unit $$i$$ is defined as $$i = \\sqrt{-1}$$ .

Simplify the expression $$(3 - i)(4 + 5i)$$ .

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

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

The modulus is given by $$|a + bi| = \\sqrt{a^2 + b^2}$$ .

What does it mean for two complex numbers to be equal?

Two complex numbers $$a + bi$$ and $$c + di$$ are equal if and only if $$a = c$$ and $$b = d$$ .

What is the result of multiplying a complex number by 1?

The result is the complex number itself, i.e., $$(a + bi) \\times 1 = a + bi$$ .

What is the result of multiplying a complex number by 0?

The result is 0, i.e., $$(a + bi) \\times 0 = 0$$ .

Simplify the expression $$(3 - i)(4 + 5i)$$ .

The expression simplifies to $$(12 + 15i - 4i - 5) = 7 + 11i$$ .

What is the distributive property in the context of complex numbers?

The distributive property states that for any complex numbers $$a, b, c$$ : $$a(b + c) = ab + ac$$ .

What is the significance of the imaginary unit in complex multiplication?

The imaginary unit allows for the representation of numbers that cannot be expressed on the real number line, enabling solutions to equations like $$x^2 + 1 = 0$$ .

Multiplying Complex Numbers Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

Define a complex number.

Back

Tags

CCSS.HSN.CN.A.1

2.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSN.CN.A.2

3.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSN.CN.C.8

4.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSN.CN.A.1

5.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSN.CN.A.3

6.

FLASHCARD QUESTION

Front

How do you multiply a complex number by its conjugate?

Back

Tags

CCSS.HSN.CN.A.3

7.

FLASHCARD QUESTION

Front

What is the result of multiplying two complex conjugates?

Back

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