====== Question 5, Exercise 1.1 ======
Solutions of Question 5 of Exercise 1.1 of Unit 01: Complex Numbers. This is unit of A Textbook of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board (KPTB or KPTBB) Peshawar, Pakistan.
=====Question 5(i)=====
Multiply the complex number $8i+11,-7+5i$.
====Solution====
\begin{align}&(8i+11)\times (-7+5i)\\
&=\left( 11+8i \right)\times \left( -7+5i \right)\\
&=\left( -77+40{{i}^{2}} \right)+\left( 55-56 \right)i\\
&=\left( -77+40\left( -1 \right) \right)+\left( 55-56 \right)i\\
&=\left( -77-40 \right)+\left( 55-56 \right)i\\
&=-117-i\end{align}

=====Question 5(ii)=====
Multiply the complex number $3i,2\left( 1-i \right)$.
====Solution====
\begin{align}&3i\times 2\left( 1-i \right)\\
&=3i\times \left( 2-2i \right)\\
&=3i\times 2-3i\times 2i\\ 
&=-6{{i}^{2}}+6i\\
&=-6\left( -1 \right)+6i\\
&=6+6i\end{align}

=====Question 5(iii)=====
Multiply the complex number $\sqrt{2}+\sqrt{3i},2\sqrt{2}-\sqrt{3i}$.
====Solution====
\begin{align}&\left( \sqrt{2}+\sqrt{3}i \right)\times \left( 2\sqrt{2}-\sqrt{3}i \right) \\
&=\left( \sqrt{2}\times 2\sqrt{2}-\sqrt{3}\times \sqrt{3}{{i}^{2}} \right)\\
&\quad +\left( \sqrt{3}\times 2\sqrt{2}-\sqrt{2}\times \sqrt{3} \right)i\\
&=\left( 4-3\left( -1 \right) \right)+\left( 2\sqrt{6}-\sqrt{6} \right)i\\
&=\left( 4+3 \right)+\sqrt{6}i\\
&=7+\sqrt{6}i\end{align}

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