Question 4, Exercise 1.1

Solutions of Question 4 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.

Subtract the second complex number from first $\left( a,0 \right)\left( 2,-b \right)$.

$$\begin{align}&\left( a,0 \right)-\left( 2,-b \right)\\ &=\left( a+0i \right)-\left( 2-bi \right)\\ &=\left( a-2 \right)+\left( 0+b \right)i\\ &=\left( a-2 \right)+bi\end{align}$$

Subtract the second complex number from first $\left( -3,\dfrac{1}{2} \right)\left( 3,\dfrac{1}{2} \right)$.

$$\begin{align}&\left( -3,\dfrac{1}{2} \right)-\left( 3,\dfrac{1}{2} \right)\\ &=\left( -3+\dfrac{1}{2}i \right)-\left( 3+\dfrac{1}{2}i \right)\\ &=\left( -3-3 \right)+\left( \dfrac{1}{2}-\dfrac{1}{2} \right)i\\ &=-6+0i\end{align}$$

Subtract the second complex number from first $3\sqrt{3}-5\sqrt{7}i,\sqrt{3}+2\sqrt{7}i$.

$$\begin{align}&\left(3\sqrt{3}-5\sqrt{7}i \right)-\left( \sqrt{3}+2\sqrt{7}i \right)\\ &=\left( 3\sqrt{3}-\sqrt{3} \right)-\left( 5\sqrt{7}+2\sqrt{7} \right)i\\ &=2\sqrt{3}-7\sqrt{7}i\end{align}$$

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