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.

Multiply the complex number $8i+11,-7+5i$.

$$\begin{align}&(8i+11)\times (-7+5i)\\ &=\left( 11+8i \right)\times \left( -7+5i \right)\\ &=\left( -77+40{{i}^{2}} \right)+\left( 55-56 \right)i\\ &=\left( -77+40\left( -1 \right) \right)+\left( 55-56 \right)i\\ &=\left( -77-40 \right)+\left( 55-56 \right)i\\ &=-117-i\end{align}$$

Multiply the complex number $3i,2\left( 1-i \right)$.

$$\begin{align}&3i\times 2\left( 1-i \right)\\ &=3i\times \left( 2-2i \right)\\ &=3i\times 2-3i\times 2i\\ &=-6{{i}^{2}}+6i\\ &=-6\left( -1 \right)+6i\\ &=6+6i\end{align}$$

Multiply the complex number $\sqrt{2}+\sqrt{3i},2\sqrt{2}-\sqrt{3i}$.

$$\begin{align}&\left( \sqrt{2}+\sqrt{3}i \right)\times \left( 2\sqrt{2}-\sqrt{3}i \right) \\ &=\left( \sqrt{2}\times 2\sqrt{2}-\sqrt{3}\times \sqrt{3}{{i}^{2}} \right)\\ &\quad +\left( \sqrt{3}\times 2\sqrt{2}-\sqrt{2}\times \sqrt{3} \right)i\\ &=\left( 4-3\left( -1 \right) \right)+\left( 2\sqrt{6}-\sqrt{6} \right)i\\ &=\left( 4+3 \right)+\sqrt{6}i\\ &=7+\sqrt{6}i\end{align}$$

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