What is the modulus of a complex number?

The modulus of a complex number $$a + bi$$ is given by $$|a + bi| = \sqrt{a^2 + b^2}$$ . It represents the distance from the origin in the complex plane.

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.

How do you express a square root of a negative number in terms of complex numbers?

To express a square root of a negative number, use the imaginary unit. For example, $$\sqrt{-x} = i\sqrt{x}$$ .

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

The result is $$(3 + 2) + (4 - 3)i = 5 + 1i$$ .

What is the result of $$(5 - 2i) - (3 + 4i)$$ ?

The result is $$(5 - 3) + (-2 - 4)i = 2 - 6i$$ .

What is $$\sqrt{-16}$$ in the form $$a + bi$$ ?

In the form $$a + bi$$ , $$\sqrt{-16} = 0 + 4i$$ , so $$a = 0$$ and $$b = 4$$ .

What is $$\sqrt{-4}$$ ?

$$\sqrt{-4} = 0 + 2i$$ , so it can be expressed as $$2i$$ .

Algebra 2 | Unit 3 | Lesson 12: Arithmetic with Complex Numbers

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1.

FLASHCARD QUESTION

Front

What is a complex number?

Back

2.

FLASHCARD QUESTION

Front

How do you add complex numbers?

Back

3.

FLASHCARD QUESTION

Front

How do you subtract complex numbers?

Back

4.

FLASHCARD QUESTION

Front

What is the imaginary unit?

Back

5.

FLASHCARD QUESTION

Front

How do you multiply complex numbers?

Back

6.

FLASHCARD QUESTION

Front

What is the conjugate of a complex number?

Back

7.

FLASHCARD QUESTION

Front

How do you divide complex numbers?

Back

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Algebra 2 | Unit 3 | Lesson 12: Arithmetic with Complex Numbers | Practice Problems

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