How do you perform the operation and write the result in standard form given #(3+sqrt(-5))(7-sqrt(-10))#?

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Answer 1 · 2017-05-07T02:23:25

#(3+sqrt(-5))(7-sqrt(-10))=(21+5sqrt2)-(3sqrt10+7sqrt5)i#

#(3+sqrt(-5))(7-sqrt(-10))#

= #3×7-3×sqrt(-10)-7sqrt(-5)+sqrt(-5)sqrt(-10)#

= #21-3sqrt((-1)×10)-7sqrt((-1)×5)+sqrt((-5)×(-10))#

= #21-3sqrt10×sqrt(-1)-7sqrt5×sqrt(-1)+sqrt50#

= #(21+sqrt50)-(3sqrt10+7sqrt5)sqrt(-1)#

= #(21+5sqrt2)-(3sqrt10+7sqrt5)i#

as #sqrt(-1)=i#