Question 1207483
<pre>
Simplify the square root. Write your answer in the form a + bi. 

sqrt{(4 + 3i)(3i - 4)}

Do I FOIL the radicand?

Yes. FOILing the radicand is pivotal in determining the answer.
Correct answer: {{{highlight_green(matrix(1,1, 0 +- 5i)))}}}

{{{matrix(3,1, sqrt((4 + 3i)(3i - 4)),
sqrt(12i - 16 + 9i^2 - 12i),
sqrt(9i^2 - 16)
)}}}
{{{sqrt(9(- 1) - 16)}}} ----- i<sup>2</sup> = - 1
{{{matrix(1,11, sqrt(- 9 - 16), "=", sqrt(- 25), "=", sqrt(- 1) * sqrt(25), "=", 
sqrt(- 1) * " " +- sqrt(25), "=", " " +- 5i, "=", highlight(0 +- 5i))}}}


<font color = blue<><font size = 4><b><u>CHECK</font></font></b></u>
Squaring {{{" " +- 5i}}} gives:    {{{matrix(2,7, (5i)^2, "=", 25i^2, "=", 25(- 1), "=", - 25, (- 5i)^2, "=", 25i^2, "=", 25(- 1), "=", - 25)}}}</pre>