Intro to Imaginary Numbers 12/13/24

Front

What is an imaginary number?

Back

An imaginary number is a number that can be written as a real number multiplied by the imaginary unit 'i', where i is defined as the square root of -1.

Front

What is the value of i^2?

Back

i^2 = -1.

Front

How do you simplify the expression i^n for n = 55?

Back

To simplify i^55, divide 55 by 4. The remainder is 3, so i^55 = i^3 = -i.

Front

What is the product of (3i) and (-2 + 4i)?

Back

(3i)(-2 + 4i) = -6i + 12i^2 = -6i - 12 = -12 - 6i.

Front

How do you simplify the square root of a negative number, such as √-8?

Back

To simplify √-8, factor out -1: √-8 = √(8) * √(-1) = 2√2 * i = 2i√2.

Front

What is the simplified form of √-23?

Back

√-23 = √(23) * √(-1) = i√23.

Front

How do you solve the equation x^2 + 81 = 0?

Back

Rearranging gives x^2 = -81. Taking the square root gives x = ±9i.

Front

What is the imaginary unit 'i'?

Back

The imaginary unit 'i' is defined as i = √-1.

Front

What is the relationship between complex numbers and imaginary numbers?

Back

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

Front

How do you add two complex numbers, such as (2 + 3i) and (4 - 5i)?

Back

To add complex numbers, combine the real parts and the imaginary parts: (2 + 3i) + (4 - 5i) = (2 + 4) + (3 - 5)i = 6 - 2i.