1.

Express with rational denominator((a+sqrt(-1))^3-(a-sqrt(-1))^3)/((a+sqrt(-1))^2-(a-sqrt(-1))^2)

Answer»

Solution :`((a+sqrt(-1))^3-(a-sqrt(-1))^3)/((a+sqrt(-1))^2-(a-sqrt(-1))^2)`
`=((a+i)^3-(a-i)^3)/((a+i)^2-(a-1)^2)`
`=(2(3a^2I=i^3))/(4ai)=(2i(3a^2-1))/(4ai)=(3a^2-1)/(2A)`


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