Section 1-8: Add, Subtract, Multiply 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

How do you add complex numbers?

Back

To add complex numbers, combine the real parts and the 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 the real parts and the 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) and (c + di) is given by (ac - bd) + (ad + bc)i.

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 a complex number by a real number?

Back

To multiply a complex number by a real number, multiply both the real and imaginary parts by that real number. For example, k(a + bi) = ka + kbi.

Front

What is the simplified form of (8 + 2i) + (1 - 6i) - (-8 - 8i)?

Back

17 + 4i.

Front

What is the simplified form of (-9 + 5i) + (3 - 2i)?

Back

-6 + 3i.

Front

Multiply: 3i(-2 + 4i)

Back

-12 - 6i.

Front

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

Back

5 + 14i.