Question

Rationalize the Denominator
2i/i-2

Answer 1

`(2i)/(i-2)=(2-4i)/(5)`

Explanation:

• 
  `(2i)/(i-2)` (Given)

• 
  `=(2i)/(i-2)* (i+2)/(i+2)` [Multiply numerator and denominator both by (i + 2)]

• 
  `=(2i(i+2))/((i-2)(i+2))`

• 
  `=(2i^2+4i))/(i^2-2^2)`

• 
  `=(2(-1)+4i))/(-1-4)`

• 
  `=(-2+4i))/(-5)`

• 
  `=(2-4i))/(5)`

• 
  `\implies (2i)/(i-2)=(2-4i)/(5)`

Answer 2

2-4i/5

Explanation:

`(2i)/(i-2) *(i+2)/(i+2)\\=(2i(i+2))/(i^2-4)\\= (2i(i+2))/(-1-4)\\ =(2i(i+2))/(-5) \\ = (-2 + 4i)/(-5)\\ =( 2 - 4i )/ 5`