Question

Show all work to multiply (3+√-16)(6√-64)

Answer 1

Answer:

$\large\boxed{(3+\sqrt{-16})(6\sqrt{-64})=-192+144i}$

Step-by-step explanation:

$\sqrt{-1}=i\to i^2=-1\\\\(3+\sqrt{-16})(6\sqrt{-64})=(3+\sqrt{(16)(-1)})(6\sqrt{(64)(-1)})\\\\=(3+\sqrt{16}\cdot\sqrt{-1})(6\cdot\sqrt{64}\cdot\sqrt{-1})=(3+4i)\bigg((6)(8i)\bigg)\\\\=(3+4i)(48i)\qquad\text{use the distributive property}\ (b+c)a=ba+ca\\\\=(3)(48i)+(4i)(48i)=144+192i^2\\\\=144i+192(-1)=-192+144i$