How do you simplify $$\sqrt{-a}$$ ?

$$\sqrt{-a} = \sqrt{a}i$$ , where a is a positive real number.

What is a complex number?

A complex number is a number that has a real part and an imaginary part, expressed as $$a + bi$$ , where a and b are real numbers.

What is the imaginary unit 'i'?

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

Simplify $$\sqrt{6i}$$ .

$$\sqrt{6i} = \sqrt{6} \cdot \sqrt{i}$$ .

How do you express a complex number in standard form?

A complex number is expressed in standard form as $$a + bi$$ , where a is the real part and b is the imaginary part.

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

The conjugate of a complex number $$a + bi$$ is $$a - bi$$ .

What happens when you multiply a complex number by its conjugate?

When you multiply a complex number by its conjugate, the result is a non-negative real number: $$(a + bi)(a - bi) = a^2 + b^2$$ .

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

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

Simplify Imaginary Numbers Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

What is an imaginary number?

Back

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CCSS.HSN.CN.A.1

2.

FLASHCARD QUESTION

Front

Back

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CCSS.HSN.CN.A.1

3.

FLASHCARD QUESTION

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CCSS.HSN.CN.A.1

4.

FLASHCARD QUESTION

Front

Back

5.

FLASHCARD QUESTION

Front

Back

6.

FLASHCARD QUESTION

Front

What is the principal square root of a negative number?

Back

The principal square root of a negative number is expressed in terms of 'i', the imaginary unit.

7.

FLASHCARD QUESTION

Front

What is the relationship between real numbers and imaginary numbers?

Back

Real numbers can be represented on a number line, while imaginary numbers are represented on a perpendicular axis, forming the complex plane.

Tags

CCSS.HSN.CN.A.1

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