Write the expression in the standard form a + bi.
-$\frac { 6 + 2 i } { 7 - 9 i }$
A) $- \frac { 3 } { 8 } + \frac { 17 } { 16 } \mathrm { i }$
B) $\frac { 12 } { 65 } + \frac { 34 } { 65 } \mathrm { i }$
C) $\frac { 12 } { 13 } + \frac { 8 } { 13 } \mathrm { i }$
D) $- \frac { 15 } { 8 } + \frac { 17 } { 16 } \mathrm { i }$

Question

Quizplus · Accepted Answer

To express $\frac { 6 + 2 i } { 7 - 9 i }$ in the standard form $a + bi$, multiply both the numerator and the denominator by the conjugate of the denominator, which is $7 + 9i$. This results in $\frac{(6+2i)(7+9i)}{(7-9i)(7+9i)}$, simplifying to $\frac{42+54i+14i+18i^2}{49+81}$, where $i^2 = -1$. This further simplifies to $\frac{42+68i-18}{130}$, or $\frac{24+68i}{130}$, which simplifies to $\frac{12}{65} + \frac{34}{65}i$, matching option B.

Write the Expression in the Standard Form a + Bi 6+2i7−9i\frac { 6 + 2 i } { 7 - 9 i }7−9i6+2i​

Write the Expression in the Standard Form a + Bi $\frac { 6 + 2 i } { 7 - 9 i }$