Adding and Multiplying Imaginary Numbers HannaD7

Front

What is an imaginary number?

Back

An imaginary number is a number that can be written as a real number multiplied by the imaginary unit 'i', where i is defined as the square root of -1.

Front

What is the value of i^2?

Back

i^2 = -1.

Front

How do you add two imaginary numbers?

Back

To add two imaginary numbers, combine their coefficients. For example, (3i + 2i) = 5i.

Front

How do you multiply two imaginary numbers?

Back

To multiply two imaginary numbers, use the distributive property and the fact that i^2 = -1. For example, (2i)(3i) = 6i^2 = -6.

Front

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

Back

(2 + 3i) + (4 + 5i) = (2 + 4) + (3i + 5i) = 6 + 8i.

Front

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

Back

(1 + 2i)(3 + 4i) = 3 + 4i + 6i + 8i^2 = 3 + 10i - 8 = -5 + 10i.

Front

What is the conjugate of a complex number?

Back

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

Front

How do you simplify (3 + 4i) - (1 + 2i)?

Back

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

Front

What is the modulus of a complex number?

Back

The modulus of a complex number a + bi is given by √(a^2 + b^2).

Front

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

Back

(5i)(-2i) = -10i^2 = 10.