Answer
$(6+5\sqrt {2})+(-2\sqrt {10}+3\sqrt {5})i$
Work Step by Step
$(2+\sqrt {-5})(3-\sqrt {-10})$
$=2(3-\sqrt {-10})+\sqrt {-5}(3-\sqrt {-10})$
$=6-2\sqrt {-10}+3\sqrt {-5}-\sqrt {-5}\sqrt {-10}$
$=6-2\sqrt {-1\times10}+3\sqrt {-1\times5}-i^{2}\sqrt {5\times10}$
$=6-2i\sqrt {10}+3i\sqrt {5}-(-1)\sqrt {50}$
$=6-2i\sqrt {10}+3i\sqrt {5}+\sqrt {2\times25}$
$=6-2i\sqrt {10}+3i\sqrt {5}+5\sqrt {2}$
$=(6+5\sqrt {2})+(-2\sqrt {10}+3\sqrt {5})i$