How do you add two complex numbers (a + bi) + (c + di)?

Add the real parts and the imaginary parts: (a + c) + (b + d)i.

How do you subtract two complex numbers (a + bi) - (c + di)?

Subtract the real parts and the imaginary parts: (a - c) + (b - d)i.

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

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

What is the polar form of a complex number?

The polar form is expressed as $$r(\text{cos}(\theta) + i\text{sin}(\theta))$$ , where r is the modulus and θ is the argument.

What is the argument of a complex number a + bi?

The argument is the angle θ formed with the positive x-axis, calculated as $$\theta = \text{tan}^{-1}(\frac{b}{a})$$ .

Complex Numbers Review Flashcards: 15 Cards (11th Grade)

Student preview

15 questions

Show all answers

1.

FLASHCARD QUESTION

Front

What is the imaginary unit 'i'?

Back

The imaginary unit 'i' is defined as $i = \frac{\text{sqrt}(-1)}{1}$ . It is used to represent the square root of negative numbers.

2.

FLASHCARD QUESTION

Front

What is the result of $\text{sqrt}(-a^2)$ ?

Back

The result is $ai$ , where 'a' is a real number.

3.

FLASHCARD QUESTION

Front

How do you multiply two complex numbers (a + bi)(c + di)?

Back

Use the distributive property: (a + bi)(c + di) = ac + adi + bci + bdi^2, and remember that $i^2 = -1$ .

4.

FLASHCARD QUESTION

Front

What is the result of $i^2$ ?

Back

The result is -1.

5.

FLASHCARD QUESTION

Front

What is the simplified form of $-6i \times 3i$ ?

Back

The simplified form is 18.

6.

FLASHCARD QUESTION

Front

What is the result of multiplying 2i by -3i?

Back

The result is -6.

7.

FLASHCARD QUESTION

Front

How do you simplify $\text{sqrt}(-25)$ ?

Back

The simplified form is 5i.

8.

FLASHCARD QUESTION

Front

What is the result of $\text{sqrt}(-36)$ ?

Back

The result is 6i.

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