Question

porfa ayudenmen a responder esta tarea

Answer 1

Explicación paso a paso:

Sabemos:

$i=\sqrt{-1}$

$i^{2} =-1$

a. $\sqrt{36*i^{2} } -\sqrt{9*i^{2} } -\sqrt{16*i^{2} }$

 $6i-3i-2i$

 $i$

b. $-\sqrt{100*i^{2} } +\sqrt{4*i^{2} } -\sqrt{25*i^{2} }$

 $-10i+2i-5i$

 $-13i$

c. $-3\sqrt{64*i^{2} } -2\sqrt{100*i^{2} } +\sqrt{36*i^{2} }$

 $-3(8i)-2(10i)+6i$

 $-24i-20i+6i$

 $-38i$

d. $-\sqrt{8*i^{2} } -\sqrt{2*i^{2} } -\sqrt{32*i^{2} } +6\sqrt{2}$

 $-2\sqrt{2} i-\sqrt{2} i-4\sqrt{2}i +6\sqrt{2}$

 $-7\sqrt{2} i+6\sqrt{2}$

 $\sqrt{2} (6-7i)$

e. $\frac{1}{2} \sqrt{3*i^{2} } -\frac{1}{5}\sqrt{125*i^{2}  } -\frac{1}{4} \sqrt{108*i^{2} }$

 $\frac{1}{2} \sqrt{3} i-\frac{1}{5} 5\sqrt{5} i-\frac{1}{4} 6\sqrt{3} i$

 $\frac{10}{20} \sqrt{3} i-\frac{4}{20} 5\sqrt{5} i-\frac{5}{20} 6\sqrt{3} i$

 $\frac{i(10\sqrt{3}-20\sqrt{5}-30\sqrt{3})}{20}$

 $\frac{i(-20\sqrt{5}-20\sqrt{3})}{20}$

 $i(-\sqrt{5} -\sqrt{3} )$

f. $\frac{4}{5} \sqrt{5*i^{2} } -\sqrt{5*i^{2} } +3\sqrt{20*i^{2} }$

 $\frac{4}{5} \sqrt{5} i-5i+6\sqrt{5} i$

 $\frac{4}{5} \sqrt{5} i-\frac{25}{5} i+\frac{30}{5} \sqrt{5} i$

 $\frac{i(4\sqrt{5}-25+30\sqrt{5} ) }{5}$

 $\frac{i(34\sqrt{5}-25) }{5}$

g. $\frac{2}{9} \sqrt{16*i^{2} } -\sqrt{4*i^{2} } -\frac{1}{9} \sqrt{36*i^{2} } +\sqrt{2*i^{2} }$

 $\frac{2}{9} 4i-2i-\frac{1}{9} 6i+\sqrt{2} i$

 $\frac{2}{9} 4i-\frac{9}{9} 2i-\frac{1}{9} 6i+\frac{9}{9}\sqrt{2} i$

 $\frac{i(8-18-6+9\sqrt{2}) }{9}$

 $\frac{i(9\sqrt{2}-16) }{9}$