How do you subtract this and answer using standard form of a complex number(a+bi)?

Question

#(3+2sqrt(54))-(-2-sqrt(-24))#

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Answer 1 · 2016-12-20T11:06:56

#color(blue)(5+6sqrt6)+color(green)(2sqrt6)color(red)i#

The standard form is #color(blue)a+color(green)bcolor(red)i#

#(3+2sqrt54)-(-2-sqrt(-24))#

Distribute the negative

#=(3+2sqrt54)+2+sqrt(-24)#

#=3+2sqrt54+2+sqrt(-24)#

Add like terms

#=5+2sqrt54+sqrt(-24)#

#color(brown)(sqrt(-24)=isqrt(24))#

#=5+2sqrt54+isqrt(24)#

You can stop here and your answer would be #color(blue)(5+2sqrt54)+color(green)(sqrt(24))color(red)i#, or you can simplify the radicals (optional)

#5+2sqrt54+isqrt(24)#

#=5+2sqrt(9*6)+isqrt(4*6)#

#=5+2sqrt9sqrt6+isqrt4sqrt6#

#=5+2*3sqrt6+i*2sqrt6#

#=5+6sqrt6+2isqrt6#

#=5+6sqrt6+2sqrt6i#

and your answer in the standard form would be #color(blue)(5+6sqrt6)+color(green)(2sqrt6)color(red)i#