456,047 views
25 votes
25 votes
Rationalize the Denominator
2i/i-2

User Edgar Bonet
by
2.9k points

2 Answers

10 votes
10 votes

Answer:


(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)
User GunnerFan
by
3.0k points
22 votes
22 votes

Answer:

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

User Mavrck
by
2.8k points
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