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Question
If \[x + iy = \frac{3 + 5i}{7 - 6i},\] then y =
Options
9/85
−9/85
53/85
none of these
Solution
\[\frac{53}{85}\]
\[x + iy=\frac{3 + 5i}{7 - 6i}\]
\[\Rightarrow x+iy=\frac{3 + 5i}{7 - 6i}\times\frac{7 + 6i}{7 + 6i}\]
\[ \Rightarrow x+iy=\frac{21 + 53i + 30 i^2}{49 - 36 i^2}\]
\[ \Rightarrow x+iy=\frac{21 - 30 + 53i}{49 + 36}\]
\[ \Rightarrow x+iy=\frac{- 9}{85}+ i\frac{53}{85}\]
\[\text { On comparing both the sdes: } \]
\[y=\frac{53}{85}\]
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