Section 1-8: Add, Subtract, Multiply Complex Numbers

Front

What are complex numbers?

Back

Complex numbers are numbers that have a real part and an imaginary part, expressed in the form a + bi, where a is the real part and b is the imaginary part.

Front

How do you add complex numbers?

Back

To add 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 complex numbers?

Back

To subtract 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 product of two complex numbers?

Back

The product of two complex numbers (a + bi)(c + di) is calculated using the distributive property: ac + adi + bci + bdi^2, where i^2 = -1.

Front

What is the conjugate of a complex number?

Back

The conjugate of a complex number a + bi is a - bi. It is used to simplify division of complex numbers.

Front

How do you multiply complex numbers?

Back

To multiply complex numbers, use the distributive property and remember that i^2 = -1. For example, (a + bi)(c + di) = ac + (ad + bc)i + bdi^2.

Front

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

Back

The simplified form is 6 - 2i.

Front

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

Back

The simplified form is -2 - 2i.

Front

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

Back

The result is 11 - 10i.

Front

How do you simplify 8i(2 + 3i) + 6i(2 + i)?

Back

The simplified form is -30 + 28i.