Complex Numbers: Simplifying, Adding, and Subtracting

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 two complex numbers?

Back

To add two complex numbers, add their real parts and their imaginary parts separately. For example, (a + bi) + (c + di) = (a + c) + (b + d)i.

Front

How do you subtract two complex numbers?

Back

To subtract two 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 result of i^2?

Back

The result of i^2 is -1.

Front

What is i^4?

Back

The result of i^4 is 1.

Front

How do you simplify i^n for n = 52?

Back

Since i^4 = 1, you can simplify i^52 as follows: i^52 = (i^4)^(13) = 1^13 = 1.

Front

How do you simplify i^n for n = 66?

Back

Since i^4 = 1, you can simplify i^66 as follows: i^66 = (i^4)^(16) * i^2 = 1^16 * (-1) = -1.

Front

What is the result of (-7 + 9i) + (2 - 10i)?

Back

The result is -5 - i.

Front

What is the result of (4 + 7i) - (3 + 2i)?

Back

The result is 1 + 5i.