AI tutor
Welcome to Bytelearn!
Let’s check out your problem:
Express the radical using the imaginary unit, . Express your answer in simplified form.
Full solution
Q. Express the radical using the imaginary unit, . Express your answer in simplified form.
- Recognize and Rewrite Expression: First, we recognize that the square root of a negative number involves the imaginary unit , where . We can rewrite the expression by factoring out from under the radical to separate the real and imaginary parts.
- Replace with Imaginary Unit: Next, we know that is the definition of the imaginary unit . So we can replace with and continue simplifying the expression.
- Simplify Square Root of : Now, we look to simplify . Since is not a perfect square, we check if it has any square factors. The prime factorization of is , which does not contain any repeated factors, so cannot be simplified further.Therefore, the expression remains as .
More problems from Introduction to complex numbers
QuestionGet tutor help
QuestionGet tutor help