Flashcard 4.4 Operations on 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

What is the imaginary unit 'i'?

Back

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

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

Back

The simplified form is -6 + 3i.

Front

How do you multiply complex numbers?

Back

To multiply complex numbers, use the distributive property (FOIL method) and apply the fact that i^2 = -1. For example, (a + bi)(c + di) = ac + adi + bci + bdi^2.

Front

What is the simplified form of (8 - 3i)²?

Back

The simplified form is 55 - 48i.

Front

What does it mean to simplify a complex number?

Back

Simplifying a complex number involves combining like terms and expressing it in the standard form a + bi.

Front

What is the conjugate of a complex number?

Back

The conjugate of a complex number a + bi is a - bi. It is used in division to eliminate the imaginary part.

Front

How do you find the conjugate of (3 + 4i)?

Back

The conjugate of (3 + 4i) is (3 - 4i).

Front

What is the result of multiplying a complex number by its conjugate?

Back

The result is a real number. For example, (a + bi)(a - bi) = a² + b².