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

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

1 Answer
Dec 20, 2016

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

Explanation:

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