Question

write the number \\(\sqrt{-16} - 8\\) in standard form and identify the parts of the complex number. use the keypad to enter your answers in the boxes. the standard form of the number \\(\sqrt{-16} - 8\\) is \\(square\\). in this form, \\(square\\) and \\(square\\) are real numbers and \\(square\\) is an imaginary number.

Explanation:

Step1: Simplify the radical term

Recall that $\sqrt{-1} = i$, so $\sqrt{-16} = \sqrt{16 \times (-1)} = \sqrt{16} \times \sqrt{-1} = 4i$.

Step2: Rearrange into standard complex form

Standard form of a complex number is $a + bi$, where $a$ is the real part and $bi$ is the imaginary part. Rearrange the given expression: $\sqrt{-16} - 8 = -8 + 4i$.

Step3: Identify real and imaginary parts

In $-8 + 4i$, the real numbers are the constant real part and the coefficient of the imaginary unit, and the imaginary number is the term with $i$.

Answer:

The standard form of the number $\sqrt{-16} - 8$ is $\boldsymbol{-8 + 4i}$.
In this form, $\boldsymbol{-8}$ and $\boldsymbol{4}$ are real numbers and $\boldsymbol{4i}$ is an imaginary number.