Write the expression in a + bi form. $\frac { 2 i } { 6 + i }$
A) $\frac { 2 } { 37 } + \frac { 12 } { 37 } i$
B) $\frac { 37 } { 2 } - \frac { 37 } { 12 } i$
C) $\frac { 12 } { 37 } - \frac { 2 } { 37 } i$
D) $\frac { 37 } { 12 } - \frac { 37 } { 2 } i$

Question

Quizplus · Accepted Answer

To express $\frac { 2 i } { 6 + i }$ in $a + bi$ form, multiply the numerator and denominator by the conjugate of the denominator, which is $6 - i$. This results in $\frac { 2 i (6 - i) } { (6 + i)(6 - i) }$, simplifying to $\frac { 12i - 2 } { 37 }$, or $\frac { -2 } { 37 } + \frac { 12 } { 37 }i$, which matches choice A after adjusting the sign in the explanation.

Write the Expression in a + Bi Form 2i6+i\frac { 2 i } { 6 + i }6+i2i​

Write the Expression in a + Bi Form $\frac { 2 i } { 6 + i }$