Simplifying Imaginary Numbers

Front

What is an imaginary number?

Back

An imaginary number is a complex 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

The value of i^2 is -1.

Front

How do you simplify the square root of a negative number, such as √-20?

Back

To simplify √-20, you can express it as √(20) * √(-1), which equals √20 * i.

Front

What is the simplified form of √-16?

Back

The simplified form of √-16 is 4i.

Front

What is the result of multiplying two imaginary numbers, such as (3i)(2i)?

Back

The result of (3i)(2i) is 6i^2, which simplifies to 6(-1) = -6.

Front

How do you express the square root of a positive number in terms of imaginary numbers?

Back

The square root of a positive number, such as √a, can be expressed as √a * 1, where 1 is the real part.

Front

What is the relationship between real numbers and imaginary numbers in the complex plane?

Back

In the complex plane, real numbers are represented on the horizontal axis, while imaginary numbers are represented on the vertical axis.

Front

What is the result of i^4?

Back

The result of i^4 is 1, since i^4 = (i^2)^2 = (-1)^2 = 1.

Front

How do you simplify expressions involving i, such as 5i + 3i?

Back

To simplify 5i + 3i, you combine like terms to get 8i.

Front

What is the value of 12i^2?

Back

The value of 12i^2 is -12, since i^2 = -1.