Question

Rationalize the Denominator 2i/i-2

Answer 1

Answer:

2-4i/5

Step-by-step explanation:

$\frac{2i}{i-2} *\frac{i+2}{i+2}\\=\frac{2i(i+2)}{i^2-4}\\= \frac{2i(i+2)}{-1-4}\\ =\frac{2i(i+2)}{-5} \\ = \frac{-2 + 4i}{-5}\\ =( 2 - 4i )/ 5$

Answer 2

Answer:

$\frac{2i}{i-2}=\frac{2-4i}{5}$

Step-by-step explanation:

• $\frac{2i}{i-2}$ (Given)

• $=\frac{2i}{i-2}\times \frac{i+2}{i+2}$ [Multiply numerator and denominator both by (i + 2)]

• $=\frac{2i(i+2)}{(i-2)(i+2)}$

• $=\frac{2i^2+4i)}{i^2-2^2}$

• $=\frac{2(-1)+4i)}{-1-4}$

• $=\frac{-2+4i)}{-5}$

• $=\frac{2-4i)}{5}$

• $\implies \frac{2i}{i-2}=\frac{2-4i}{5}$