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^n, divide n by 4 and use the remainder: i^55 = i^(4*13 + 3) = i^3 = -i.

Front

What is the square root of a negative number?

Back

Front

Back

Front

What is the product of two imaginary numbers, (2i)(3i)?

Back

(2i)(3i) = 6i^2 = 6(-1) = -6.

Front

How do you solve the equation 5x² = -75 using the square root method?

Back

First, divide both sides by 5: x² = -15. Then take the square root: x = ±i√15.

Front

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

Back

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

Front

What is the definition of the imaginary unit 'i'?

Back

The imaginary unit 'i' is defined as the square root of -1, which is used to extend the real number system to 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.