(1-√2i )(2 + √3i )=

(1-√2i )(2 + √3i )=

\((1-\sqrt{2 }\;i)(2+\sqrt{3}\;i)\\ =1(2+\sqrt{3}\;i)-\sqrt{2 }\;i(2+\sqrt{3}\;i)\\ =2+\sqrt{3}\;i\quad-2\sqrt{2 }i\;-\sqrt{2}\;i\;*\sqrt{3}\;i\\ =2+\sqrt{3}\;i\quad-2\sqrt{2 }i\;+\sqrt{6}\\ =(2+\sqrt{6})+(\sqrt{3}\;\:-2\sqrt{2 })i\;\\\)

Thank you Melody :) 

(1-√2i )(2 + √3i )= 

Square root: sqrt(3i) = 1.2247449+1.2247449i

Add: 2 + (1.2247449+1.2247449i) = 3.2247449+1.2247449i

Square root: sqrt(2i) = 1+i

Subtract: 1 - (1+i) = -i

Multiple: (3.2247449+1.2247449i) * (-i) = 1.2247449-3.2247449i