Complex Numbers Flashcard

Front

Define 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, which means i² = -1.

Front

How do you add two complex numbers?

Back

To add two complex numbers, combine their real parts and their imaginary parts separately. For example, (a + bi) + (c + di) = (a + c) + (b + d)i.

Front

How do you subtract two complex numbers?

Back

To subtract two complex numbers, subtract their real parts and their imaginary parts separately. For example, (a + bi) - (c + di) = (a - c) + (b - d)i.

Front

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

Back

The result is 6 + 2i.

Front

What is the result of (9 - 8i) - (6 + 7i)?

Back

The result is -3 - 15i.

Front

What is the result of (7 - 6i) - (2 + 3i)?

Back

The result is 5 - 9i.

Front

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

Back

The result is 2 - 6i.

Front

What is the result of (4 - 3i) - (1 + 2i)?

Back

The result is 3 - 5i.

Front

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

Back

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