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Peace to all. When I solve the problem I get $\dfrac{70} { 97}$ - $\dfrac{12{i}} {97}$ and it's the wrong answer. How exactly do you go about solving this problem?

This is my work: I received that answer by multiplying both the numerator and denominator by the conjugate partner of "-9 - 4i" which is "-9 + 4i".

$\dfrac{-54 + 24 {i} - 36{i} +16i^2} { 81 - 36 {i} + 36 {i} - 16i^2}$

Combining like terms: $\dfrac{-54 + 24 {i} - 36{i} +16(-1)} { 81 - 36 {i} + 36 {i} - 16(-1)}$ = $\dfrac{-70 - 12i} { 81 + 16}$ = $\dfrac{-70} { 97}$ - $\dfrac{12{i}} {97}$

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    $\begingroup$ Please show all your work. How did you get that number? $\endgroup$
    – azif00
    Oct 5 '21 at 1:32
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    $\begingroup$ You got a sign wrong somewhere. I'm getting that the numerator should be $-70-12i$. Your edited question has the correct answer, which is different from your original answer. $(-9-4i)(-9+4i)=81+16=97$, not $-97$. $\endgroup$ Oct 5 '21 at 1:43
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    $\begingroup$ @RobertShore As I was writing it I noticed that I didn't copy the correct sign from my work. It's those tiny minute (important) details that I overlook sometimes with math. Thank you $\endgroup$
    – יהודה
    Oct 5 '21 at 1:52
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    $\begingroup$ "$\dfrac{70 - 12 {i}} {97}$ or $\dfrac{70{i}} { 97}$ - $\dfrac{12{i}} {97}$". Why did you write "or" in between these expressions? These both expressions are different. $\dfrac{70 - 12 {i}} {97} = \dfrac{70}{97} - \dfrac{12i}{97}$. You wrongly splitted the expression. Additionally I think your intention was to write $\dfrac{-70 -12i}{97} $ not $\dfrac{70-12i}{97}$. Please edit it. $\endgroup$
    – user947346
    Oct 5 '21 at 3:01
  • $\begingroup$ @ProThala Thank you, changes made $\endgroup$
    – יהודה
    Oct 5 '21 at 17:52
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To avoid confusion, we better take out the negative sign of the denominator first and then multiply the conjugate of 9+4i.

$\displaystyle {\quad \frac{6+4i}{-9-4i}\\= -\frac{6+4i}{9+4i}\cdot\frac{9-4i}{9-4i} \\=-\frac{70+12i}{81+16} \\=-\frac{70}{97} -\frac{12}{97} i}$

$$\textrm{ :|D Wish it helps!} $$

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    $\begingroup$ (+1) nice explanation :) $\endgroup$
    – user947346
    Oct 5 '21 at 3:05
  • $\begingroup$ Thank you very much for your appreciation! $\endgroup$
    – Lai
    Oct 5 '21 at 16:17
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By multiplying both the numerator and denominator by the conjugate partner of "-9 - 4i" which is "-9 + 4i", you will get:

$\dfrac{-54 + 24 {i} - 36{i} +16i^2} { 81 - 36 {i} + 36 {i} - 16i^2}$

Then combining like terms:

$\dfrac{-54 + 24 {i} - 36{i} +16(-1)} { 81 - 36 {i} + 36 {i} - 16(-1)}$ = $\dfrac{-70 - 12i} { 81 + 16}$ = $\dfrac{-70} { 97}$ - $\dfrac{12{i}} {97}$

Hope this assists anyone who has/had similar difficulties in solving an equation similar to or like the one above.

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  • $\begingroup$ @Moo Thank you, changes made $\endgroup$
    – יהודה
    Oct 5 '21 at 17:51

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