Radicals and Rational Exponents

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 convert a radical expression to exponential form?

Back

To convert a radical expression to exponential form, use the property: √x = x^(1/2). For example, √4 = 4^(1/2).

Front

What is the exponential form of x^(1/n)?

Back

The exponential form of x^(1/n) is the nth root of x, which can be written as √[n]{x}.

Front

How do you simplify √-4?

Back

√-4 can be simplified as √(4) * √(-1) = 2i.

Front

What is the result of simplifying √(a^2)?

Back

The result of simplifying √(a^2) is |a|, the absolute value of a.

Front

What is the relationship between radicals and rational exponents?

Back

Radicals can be expressed as rational exponents. For example, √x = x^(1/2) and ∛x = x^(1/3).

Front

How do you simplify the expression (x^2)^(3)?

Back

Using the power of a power property, (x^2)^(3) simplifies to x^(2*3) = x^6.

Front

What is the simplified form of (2i)(3i)?

Back

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

Front

What is the sum of 5 + 3i and 2 - 4i?

Back

(5 + 3i) + (2 - 4i) = (5 + 2) + (3i - 4i) = 7 - i.