Which of the following is the correct notation for the complex number $1-\sqrt{-16}$ ?
A. $i-4$
B. $1-4 i$
C. $1+4 i$
D. $1-i \sqrt{\delta}$
Answer (1)
Simplify the square root: − 16 = 4 i .
Substitute back into the original expression: 1 − − 16 = 1 − 4 i .
The correct notation for the complex number is 1 − 4 i .
Explanation
Understanding the Problem We are asked to find the correct notation for the complex number 1 − − 16 . Let's simplify the expression.
Simplifying the Square Root First, we simplify the square root of -16. Recall that − 1 = i , so we have − 16 = 16 × − 1 = 16 × − 1 = 4 i .
Substituting Back Now, substitute this back into the original expression: 1 − − 16 = 1 − 4 i .
Identifying the Correct Option Comparing this result with the given options, we see that the correct notation is 1 − 4 i .
Examples
Complex numbers are used extensively in electrical engineering to analyze AC circuits. For example, the impedance of a circuit, which is a measure of its opposition to alternating current, is often expressed as a complex number. The real part represents resistance, and the imaginary part represents reactance. Understanding complex number notation allows engineers to easily calculate and manipulate these quantities to design and analyze circuits effectively.
