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

The imaginary unit 'i' is defined as i = √(-1). It is used to represent the square root of negative numbers.

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 (a + bi)(c + di)?

Back

The product is given by (ac - bd) + (ad + bc)i, using the distributive property and the fact that i^2 = -1.

Front

What is the simplified form of (11 - 7i) - (-3 + 12i)?

Back

14 - 19i.

Front

What is the result of multiplying 3i(4 - i)?

Back

3 + 12i.

Front

What is the simplified form of (-6i)(3i)?

Back

18.

Front

How do you simplify powers of 'i'?

Back

Powers of 'i' cycle every four: i^1 = i, i^2 = -1, i^3 = -i, i^4 = 1. For higher powers, reduce the exponent modulo 4.

Front

What is the simplified form of i^13?

Back

i.