1.1 Radicals and Complex Numbers

Simplifying radical expressions and solving radical equations were a focus of your previous algebra course. However, your solutions to these problems dealt with only a specific type of numbers: REAL NUMBERS.

Besides zero, anytime you multiply a real number by itself, you get a positive number as the answer.

Solving the equation should look something like the following:

Technically, it is not possible to solve for a square root of a negative number unless you use your imagination. Because only real numbers can be multiplied by themselves to yield a positive number, mathematicians created a new type of numbers. The opposite of “real” is “not real” so they are called IMAGINARY NUMBERS.

The solutions to the equation are . Mathematicians ignore the negative value and focus on as the fundamental number for imaginary numbers. This value is given a special symbol . All imaginary numbers have as a factor.

  • Key Terms
    • radicals
    • complex numbers
    • imaginary numbers

Essential Questions
  • How do the arithmetic operations on numbers extend to complex numbers?

Practice Problems