Question 926740
express the reciprocal of {{{-4 + sqrt(-50)}}} in the form of {{{(a+bi)}}}:

{{{1/(-4 + sqrt(-50))}}}

{{{(-4 - sqrt(-50))/((-4 + sqrt(-50))(-4 - sqrt(-50)))}}}

{{{(-4 - sqrt(-50))/(-4)^2  - (sqrt(-50))^2)}}}

{{{(-4 - sqrt(-50))/(16 -(-50))}}}

{{{(-4 - 5sqrt(2)i)/(66)}}}

{{{-4/66 - 5sqrt(2)i/66}}}

{{{-2/33 +5sqrt(2)i/66}}}

{{{-2/33 +5(sqrt(2))^2i/(66sqrt(2))}}}

{{{-2/33 +5*cross(2)*i/(cross(66)33sqrt(2))}}}

{{{-2/33-5i/(33sqrt(2))}}}



express the reciprocal of {{{5i}}} in the form of {{{(a+bi)}}}:

 the reciprocal of {{{5i}}} is: {{{1/5i}}}

 {{{1/5i=(1*5i)/(5i*5i)=5i/(25i^2)=5i/25(-1)=-cross(5)i/cross(25)5=-i/5}}}