How do you simplify the radical $$\frac{(4\text{√}3)}{3}$$ ?

The expression $$\frac{(4\text{√}3)}{3}$$ is already in its simplest form.

How do you add two radicals, such as $$\text{√}2 + \text{√}2$$ ?

You can add two like radicals by combining them: $$\text{√}2 + \text{√}2 = 2\text{√}2$$ .

How do you multiply two complex numbers, such as $$(2 + 3i)(1 - 4i)$$ ?

Use the distributive property: $$(2 + 3i)(1 - 4i) = 2 - 8i + 3i - 12i^2 = 2 - 5i + 12 = 14 - 5i$$ .

How do you simplify $$\text{√}12$$ ?

$$\text{√}12 = \text{√}(4 \times 3) = \text{√}4 \times \text{√}3 = 2\text{√}3$$ .

What is the result of $$\text{√}(-1)$$ ?

$$\text{√}(-1) = i$$ , where $$i$$ is the imaginary unit.

How do you solve the equation $$x^2 = 9$$ ?

Take the square root of both sides: $$x = \text{±}\text{√}9 = \text{±}3$$ .

What is the difference between rational and irrational numbers?

Rational numbers can be expressed as a fraction of two integers, while irrational numbers cannot be expressed as a simple fraction (e.g., $$\text{√}2$$ is irrational).

How do you rationalize the denominator of $$\frac{1}{\text{√}2}$$ ?

Multiply the numerator and denominator by $$\text{√}2$$ : $$\frac{1}{\text{√}2} \times \frac{\text{√}2}{\text{√}2} = \frac{\text{√}2}{2}$$ .

What is the sum of the roots of the equation $$x^2 - 5x + 6 = 0$$ ?

The sum of the roots can be found using the formula $$-b/a$$ , which gives $$5/1 = 5$$ .

How do you express a complex number in polar form?

A complex number $$a + bi$$ can be expressed in polar form as $$r(\text{cos}(\theta) + i\text{sin}(\theta))$$ , where $$r = \text{√}(a^2 + b^2)$$ and $$\theta = \text{tan}^{-1}(\frac{b}{a})$$ .

What is the product of two conjugate complex numbers?

The product of two conjugate complex numbers, such as $$(a + bi)(a - bi)$$ , is $$a^2 + b^2$$ .

Chapter 9 (Radicals and Complex Numbers) Review Flashcards

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1.

FLASHCARD QUESTION

Front

What is a radical in mathematics?

Back

A radical is an expression that includes a root, such as a square root (√) or cube root (∛). It represents the inverse operation of exponentiation.

2.

FLASHCARD QUESTION

Front

Back

3.

FLASHCARD QUESTION

Front

What is the principal square root of a number?

Back

The principal square root of a number is the non-negative root of that number. For example, the principal square root of 9 is 3.

4.

FLASHCARD QUESTION

Front

Back

5.

FLASHCARD QUESTION

Front

What is a complex number?

Back

6.

FLASHCARD QUESTION

Front

Back

7.

FLASHCARD QUESTION

Front

What is the conjugate of a complex number?

Back

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