Answer:
[tex]-10+i\sqrt{2}[/tex]
Step-by-step explanation:
One is given the following expression:
[tex]\sqrt{4}-\sqrt{-98}-\sqrt{144}+\sqrt{-128}[/tex]
In order to simplify and solve this problem, one must keep the following points in mind: the square root function ([tex]\sqrt{}[/tex]) is a way of requesting one to find what number times itself equals the number underneath the radical sign. One must also remember the function of taking the square root of a negative number. Remember the following property: ([tex]\sqrt{-1}=i[/tex]). Simplify the given equation. Factor each of the terms and rewrite the equation. Use the square root property to simplify the radicals and perform operations between them.
[tex]\sqrt{4}-\sqrt{-98}-\sqrt{144}+\sqrt{-128}[/tex]
[tex]\sqrt{2*2}-\sqrt{-1*2*7*7}-\sqrt{12*12}+\sqrt{-1*2*8*8}[/tex]
Take factors from out of under the radical:
[tex]\sqrt{2*2}-\sqrt{-1*2*7*7}-\sqrt{12*12}+\sqrt{-1*2*8*8}[/tex]
[tex]2-7i\sqrt{2}-12+8i\sqrt{2}[/tex]
Simplify,
[tex]-10+i\sqrt{2}[/tex]
