Complex Numbers

Front

What is the definition of 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.

Front

What does the imaginary unit 'i' represent?

Back

The imaginary unit 'i' represents the square root of -1.

Front

What is the value of i^2?

Back

i^2 = -1.

Front

How do you multiply two complex numbers?

Back

To multiply two complex numbers, use the distributive property (FOIL method) and combine like terms.

Front

What is the result of (3i)(5i)?

Back

(3i)(5i) = 15i^2 = 15(-1) = -15.

Front

How do you add two complex numbers?

Back

To add two complex numbers, add their real parts and their imaginary parts separately.

Front

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

Back

(3 + 2i) + (4 - 5i) = (3 + 4) + (2 - 5)i = 7 - 3i.

Front

How do you subtract two complex numbers?

Back

To subtract two complex numbers, subtract their real parts and their imaginary parts separately.

Front

What is the result of (4 - 2i) - (3 + 6i)?

Back

(4 - 2i) - (3 + 6i) = (4 - 3) + (-2 - 6)i = 1 - 8i.

Front

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

Back

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