Question

complex numbers online practice
complete this assessment to review what you’ve learned. it will not count toward
simplify the expression $(-7 - \sqrt{-100}) - (-15 - \sqrt{-81})$. (1 point)
\\(\circ\\) $8 - 19i$
\\(\circ\\) $-8 + i$
\\(\circ\\) $8 - i$
\\(\circ\\) $-22 + 19i$

Explanation:

Step1: Simplify square roots of negative numbers

Recall that \(\sqrt{-a}=\sqrt{a}\cdot i\) for \(a>0\). So, \(\sqrt{-100}=\sqrt{100}\cdot i = 10i\) and \(\sqrt{-81}=\sqrt{81}\cdot i=9i\).
Substitute these into the original expression: \((-7 - 10i)-(-15 - 9i)\)

Step2: Distribute the negative sign

Distribute the negative sign in the second parentheses: \(-7 - 10i + 15 + 9i\)

Step3: Combine like terms

Combine the real parts and the imaginary parts separately.
Real parts: \(-7 + 15=8\)
Imaginary parts: \(-10i+9i=-i\)
So the simplified expression is \(8 - i\)

Answer:

\(8 - i\) (corresponding to the option "8 − i")