Write the complex number in standard form. 9 + − 16 3 \frac{9+\sqrt{-16}}{3} 3 9 + − 16 <path d="M95,702 c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14 c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54 c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10 s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429 c69,-144,104.5,-217.7,106.5,-221 l0 -0 c5.3,-9.3,12,-14,20,-14 H400000v40H845.2724 s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7 c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z M834 80h400000v40h-400000z">

Hey, y'all. Let's take a look at this practice problem. So here, I'm asked to write the complex number in standard form. And I'm given 9 plus the square root of negative 16 divided by 3. Now we don't have any i's here right now, but remember if I have the square root of a negative number, I am dealing with an imaginary number. So let's go ahead and expand this out a little bit. So imaginary number. So let's go ahead and expand this out a little bit. So the numerator of this fraction, this 9 plus the square root of 16, I know that I can simplify this further into 9+i times the square root of 16. And further, I know that the square root of 16 is just 4, so this really just becomes 9+4i. Now taking into account our denominator as well, all of this is divided by 3. But let's simplify this even more. So I can actually separate this fraction out, and I'm gonna end up getting 9 over 3 plus 4 over 3 times I. Now I can further simplify this yet again because 9 divided by 3 is just 3. Now that 4 thirds is not going to further simplify, so it's just gonna say 4 thirds I. And now this number is in standard form because standard form is a+bi. So the standard form of this original number over here is 3+4 thirdsi. That's all for this one. I'll see you in the next one.