Simplifying Negative Radicals

Front

Define 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 i = √(-1).

Front

What is the value of i^2?

Back

i^2 = -1.

Front

Simplify: i^3.

Back

i^3 = i^2 * i = -1 * i = -i.

Front

What is the value of i^4?

Back

i^4 = (i^2)^2 = (-1)^2 = 1.

Front

Simplify: i^5.

Back

i^5 = i^4 * i = 1 * i = i.

Front

What is the principal square root of a negative number?

Back

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Front

What is the product of two imaginary numbers?

Back

The product of two imaginary numbers, such as a * i and b * i, is given by: (a * i)(b * i) = ab * i^2 = -ab.

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Back