Flashcard - Radicals and Complex Numbers

Front

What is a complex number?

Back

A complex number is a number that can be expressed in the form a + bi, where a and b are real numbers, and i is the imaginary unit, defined as the square root of -1.

Front

What is the imaginary unit 'i'?

Back

The imaginary unit 'i' is defined as the square root of -1. It is used to extend the real number system to include solutions to equations that do not have real solutions.

Front

How do you multiply two complex numbers?

Back

To multiply two complex numbers (a + bi) and (c + di), use the distributive property: (a + bi)(c + di) = ac + adi + bci + bdi^2. Remember that i^2 = -1.

Front

What is the result of (2 + 9i)(9 + 2i)?

Back

The result is 85i.

Front

What is the result of (5 - 6i)(6 + 6i)?

Back

The result is 66 - 6i.

Front

What is the result of (3 + 8i)(8 - 4i)?

Back

The result is 56 + 52i.

Front

How do you add two complex numbers?

Back

To add two complex numbers (a + bi) and (c + di), simply add the real parts and the imaginary parts: (a + bi) + (c + di) = (a + c) + (b + d)i.

Front

What is the result of (6 + 5i) + (5 + 7i)?

Back

The result is 11 + 12i.

Front

What is the result of (7 + 4i) + (4 - 8i)?

Back

The result is 11 - 4i.

Front

What is the conjugate of a complex number?

Back

The conjugate of a complex number a + bi is a - bi. It is used in division and to find the modulus.