Write the quotient in standard form. $\frac { 6 + 12 i } { 4 i }$
A)3 - $\frac { 3 } { 2 }$ i
B)3 - 3i
C)3 $+$ $\frac { 3 } { 2 }$ i
D)3i - $\frac { 3 } { 2 }$
E)3i + $\frac { 3 } { 2 }$

Question

Write the quotient in standard form. ​​ $\frac { 6 + 12 i } { 4 i }$ ​
A)3 - $\frac { 3 } { 2 }$ i
B)3 - 3i
C)3 $+$ $\frac { 3 } { 2 }$ i
D)3i - $\frac { 3 } { 2 }$
E)3i + $\frac { 3 } { 2 }$

Quizplus · Accepted Answer

To divide complex numbers, you can multiply the numerator and denominator by the conjugate of the denominator. Here, the conjugate of $4i$ is $-4i$. So, $\frac{6 + 12i}{4i} \cdot \frac{-4i}{-4i} = \frac{-24i - 48i^2}{-16i^2}$. Since $i^2 = -1$, this simplifies to $\frac{-24i + 48}{16}$ or $3 - \frac{3}{2}i$.

Write the Quotient in Standard Form 6+12i4i\frac { 6 + 12 i } { 4 i }4i6+12i​

Write the Quotient in Standard Form $\frac { 6 + 12 i } { 4 i }$