====== Question 5, Exercise 1.1 ======
Solutions of Question 5 of Exercise 1.1 of Unit 01: Complex Numbers. This is unit of Model Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Federal Textbook Board, Islamabad, Pakistan. 
====Question 5====
Find the complex number $z$ if $4z-3\bar{z}=\dfrac{1-18i}{2-i}$

**Solution.**

Suppose $z=x+iy$, then $\bar{z}=x-iy$. So we have
\begin{align}&4z-3\bar{z}=\dfrac{1-18i}{2-i}\\
\implies &4(x+iy)-3(x-iy)=\dfrac{1-18i}{2-i}\times \dfrac{2+i}{2+i}\\
\implies &4x+4iy-3x+3iy=\dfrac{(1-18i)(2+i)}{2^2-i^2} \end{align}
\begin{align} \implies x+7iy&=\dfrac{2-18i^2-36i+i}{4+1}\\
&=\dfrac{20-35i}{5}\\
&=\dfrac{5(4-7i)}{5}\\
\implies x+7iy&=4-7i\end{align}
Equating real and imaginary parts.
\begin{align}x=4 \quad \text{and}\quad 7y &=-7 \,\text{ i.e. }\,y=-1.\end{align}
Thus we have $z=x+iy=4-i$.

GOOD
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