Simplify $\frac { 2 + 5 i } { 3 i }$ and write the answer in standard form.

A) $- \frac { 5 } { 3 } - \frac { 2 i } { 3 }$

B) $\frac { 5 } { 3 } - \frac { 2 i } { 3 }$

C) $\frac { 5 } { 3 } + \frac { 2 i } { 3 }$

D) $\frac { 2 } { 3 } + \frac { 5 i } { 3 }$

E) $- \frac { 2 } { 3 } + \frac { 5 i } { 3 }$

Question

Simplify $\frac { 2 + 5 i } { 3 i }$ and write the answer in standard form.

A) $- \frac { 5 } { 3 } - \frac { 2 i } { 3 }$

B) $\frac { 5 } { 3 } - \frac { 2 i } { 3 }$

C) $\frac { 5 } { 3 } + \frac { 2 i } { 3 }$

D) $\frac { 2 } { 3 } + \frac { 5 i } { 3 }$

E) $- \frac { 2 } { 3 } + \frac { 5 i } { 3 }$

Quizplus · Accepted Answer

To simplify, we can multiply by the conjugate of the denominator, which is $-3i$. We get $$\frac{2+5i}{3i}=\frac{2+5i}{3i} \cdot \frac{-3i}{-3i} = \frac{-6i-15}{9} = -\frac{5}{3}-\frac{2i}{3}.$$ Writing this in standard form, we get $\boxed{	extbf{(B) } \frac53-\frac23i}$.

Simplify 2+5i3i\frac { 2 + 5 i } { 3 i }3i2+5i​

Simplify $\frac { 2 + 5 i } { 3 i }$