Ask Questions, Get Answers

Want to ask us a question? Click here
Browse Questions
Home  >>  TN XII Math  >>  Complex Numbers
0 votes

Find the real values of $\mathit{x}$ and $\mathit{y}$ for which the following equation: $\large\frac{\left ( 1+\mathit{i} \right )\mathit{x}-2\mathit{i}}{3+\mathit{i}} + \frac{\left ( 2-3\mathit{i} \right )\mathit{y}+\mathit{i}}{3-\mathit{i}} = $$\mathit{i}$

This is the second part of the multi-part question Q4.

Can you answer this question?

1 Answer

0 votes
  • If $a+ib=c+id$ then $a=c$ and $b=d$
  • (i.e) if $z_1=z_2$,then $Re(z_1)=Re(z_2),Im(z_1)=Im(z_2)$
  • If $z_1=a+ib$, $z_2=c+id$
  • $z_1z_2=(a+ib)(c+id)=(ac-bd)+i(ad+bc)$
  • $\mid z_1z_2\mid=\mid z_1\mid\mid z_2\mid$
Step 1:
Simplifying the terms on the LHS
$(1)+(2)$ we get
$\Rightarrow LHS= \large\frac{(4x+9y-3)+i(2x-7y-3)}{10}$$=i(RHS)$
Step 2:
Equating the real and imaginary parts and simplifying
$\Delta=\begin{vmatrix}4 & 9\\2 & -7\end{vmatrix}$
$\Delta x=\begin{vmatrix}3& 9\\13 & -7\end{vmatrix}$
$\Delta x=-138$----(3)
$\Delta y=\begin{vmatrix}4& 3\\2 & 13\end{vmatrix}$
$\Delta y=46$----(4)
Step 3:
Substitute the value of $\Delta$ in eq(3) we get
$\Delta x=-138$
Substitute the value of $\Delta$ in eq(4) we get
$\Delta y=46$
answered Jun 7, 2013 by sreemathi.v
edited Jun 7, 2013 by sreemathi.v

Related questions

Ask Question
student study plans
JEE MAIN, CBSE, AIPMT Mobile and Tablet App
The ultimate mobile app to help you crack your examinations
Get the Android App