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- Question 13, Exercise 10.1 @fsc-part1-kpk:sol:unit10
- i\cos\theta\right)\\ &=r\sin(\theta+\varphi),\\ &\text{ where } \sin\varphi=\dfrac{3}{5}, \cos\varphi=\dfrac{4}{5} \text{ and } r=5.\end{align} =====Question 13(ii)=====... i\cos\theta\right)\\ &=r\sin(\theta+\varphi),\\ &\text{ where } \sin\varphi=\dfrac{8}{17}, \cos\varphi=\dfrac{15}{17} \text{ and } r=17.\end{align} =====Question 13(iii)===
- Question 5, Exercise 10.3 @fsc-part1-kpk:sol:unit10
- circ-40^\circ) \right)\sin {{20}^{\circ }} \quad \text{by using (1)}\\ &=-\dfrac{\sqrt{3}}{4}\left( \cos... +20^\circ)-\sin(40^\circ-20^\circ) \right) \quad \text{by using (2)}\\ &=\dfrac{\sqrt{3}}{8}\sin {{20}^{... ^{\circ }}-{{10}^{\circ }} \right) \right) \quad \text{by using (1)}\\ &=-\dfrac{1}{4}\sin {{50}^{\circ ... \right)+\dfrac{1}{8}\sin {{50}^{\circ }} \quad \text{by using (2)}\\ &=-\dfrac{1}{8}\left( \sin {{130}
- Question 7, Exercise 1.2 @fsc-part1-kpk:sol:unit01
- dfrac{2+3i}{5-2i}\times \dfrac{5+2i}{5+2i} \quad \text{by rationalizing} \\ =&\dfrac{10-6+15i+4i}{25+4}\... frac{-3+4i}{1-3i}\times \dfrac{1+3i}{1+3i} \quad \text{by rationalizing}\\ =&\dfrac{-3-12+4i-9i}{1+9}\\ ... ginary part $=\dfrac{308}{169}$ ==== Go To ==== <text align="left"><btn type="primary">[[fsc-part1-kpk:sol:unit01:ex1-2-p5|< Question 6]]</btn></text> <text align="right"><btn type="success">[[fsc-pa
- Question 5, Exercise 1.2 @fsc-part1-kpk:sol:unit01
- 3bi}{2a-3bi}\times \dfrac{2a+3bi}{2a+3bi} \quad (\text{by rationalizing})\\ &=\dfrac{-2{{a}^{2}}+9{{b}^{... z}_{1}}}}{\overline{{{z}_{2}}}}.$$ ====Go to==== <text align="left"><btn type="primary">[[fsc-part1-kpk:sol:unit01:ex1-2-p3|< Question 3 & 4]]</btn></text> <text align="right"><btn type="success">[[fsc-part1-kpk:sol:unit01:ex1-2-p5|Question 6 >]]</btn></tex
- Question 6, Exercise 1.2 @fsc-part1-kpk:sol:unit01
- ht|\\ &=|{{z}_{1}}|\cdot \dfrac{1}{|{{z}_{2}}|}, \text{ by using (1)}\\ &=\dfrac{|{{z}_{2}}|}{|{{z}_{2}}|}=R.H.S.\end{align} ==== Go To ==== <text align="left"><btn type="primary">[[fsc-part1-kpk:sol:unit01:ex1-2-p4|< Question 5]]</btn></text> <text align="right"><btn type="success">[[fsc-part1-kpk:sol:unit01:ex1-2-p6|Question 7 >]]</btn></tex
- Question 8, Exercise 1.2 @fsc-part1-kpk:sol:unit01
- erline{z}=-bi \\ \implies &\overline{z}=-z \quad \text{by using (2).} \end{align} This was required. ==== Go To ==== <text align="left"><btn type="primary">[[fsc-part1-kpk:sol:unit01:ex1-2-p6|< Question 7]]</btn></text> <text align="right"><btn type="success">[[fsc-part1-kpk:sol:unit01:ex1-2-p8|Question 9 >]]</btn></tex
- Question 7, Exercise 10.2 @fsc-part1-kpk:sol:unit10
- \right)\left( 1 \right)\\ &=\cos 2\theta \quad \text{(By using double angle identity)}\\ &=\dfrac{1}{\... &=\sin 2\theta \cos 2\alpha =R.H.S.\end{align} <text align="left"><btn type="primary">[[fsc-part1-kpk:sol:unit10:ex10-2-p5|< Question 6]]</btn></text> <text align="right"><btn type="success">[[fsc-part1-kpk:sol:unit10:ex10-2-p7|Question 8, 9 >]]</btn></
- Question 2 & 3, Exercise 1.1 @fsc-part1-kpk:sol:unit01
- 1+\sqrt{2} \right)i\end{align} ====Go to ==== <text align="left"><btn type="primary">[[fsc-part1-kpk:sol:unit01:ex1-1-p1|< Question 1]]</btn></text> <text align="right"><btn type="success">[[fsc-part1-kpk:sol:unit01:ex1-1-p3|Question 4 >]]</btn></text>
- Question 4, Exercise 1.1 @fsc-part1-kpk:sol:unit01
- 7} \right)i\\ &=2\sqrt{3}-7\sqrt{7}i\end{align} <text align="left"><btn type="primary">[[fsc-part1-kpk:sol:unit01:ex1-1-p2 |< Question 2 & 3]]</btn></text> <text align="right"><btn type="success">[[fsc-part1-kpk:sol:unit01:ex1-1-p4|Question 5 >]]</btn></text>
- Question 5, Exercise 1.1 @fsc-part1-kpk:sol:unit01
- +3 \right)+\sqrt{6}i\\ &=7+\sqrt{6}i\end{align} <text align="left"><btn type="primary">[[fsc-part1-kpk:sol:unit01:ex1-1-p3|< Question 4]]</btn></text> <text align="right"><btn type="success">[[fsc-part1-kpk:sol:unit01:ex1-1-p5|Question 6 >]]</btn></text>
- Question 6, Exercise 1.1 @fsc-part1-kpk:sol:unit01
- ^{2}}}\\ &=\dfrac{-6i+1}{1}\\ &=1-6i\end{align} <text align="left"><btn type="primary">[[fsc-part1-kpk:sol:unit01:ex1-1-p4|< Question 5]]</btn></text> <text align="right"><btn type="success">[[fsc-part1-kpk:sol:unit01:ex1-1-p6|Question 7 >]]</btn></text>
- Question 7, Exercise 1.1 @fsc-part1-kpk:sol:unit01
- \dfrac{\sqrt{65}}{13}\end{align} ==== Go to==== <text align="left"><btn type="primary">[[fsc-part1-kpk:sol:unit01:ex1-1-p5|< Question 6]]</btn></text> <text align="right"><btn type="success">[[fsc-part1-kpk:sol:unit01:ex1-1-p7|Question 8 >]]</btn></text>
- Question 8, Exercise 1.1 @fsc-part1-kpk:sol:unit01
- {6}{25}+\dfrac{8i}{25}\end{align} ====Go to==== <text align="left"><btn type="primary">[[fsc-part1-kpk:sol:unit01:ex1-1-p6|< Question 7]]</btn></text> <text align="right"><btn type="success">[[fsc-part1-kpk:sol:unit01:ex1-1-p8|Question 9 & 10 >]]</btn></text>
- Question 9 & 10, Exercise 1.1 @fsc-part1-kpk:sol:unit01
- 2i-2 \right)\\ &=2-2i\end{align} ====Go to==== <text align="left"><btn type="primary">[[fsc-part1-kpk:sol:unit01:ex1-1-p7|< Question 8]]</btn></text> <text align="right"><btn type="success">[[fsc-part1-kpk:sol:unit01:ex1-1-p9|Question 11 >]]</btn></text>
- Question 2, Exercise 1.2 @fsc-part1-kpk:sol:unit01
- (4), we get the required result. ==== Go To ==== <text align="left"><btn type="primary">[[fsc-part1-kpk:sol:unit01:ex1-2-p1|< Question 1]]</btn></text> <text align="right"><btn type="success">[[fsc-part1-kpk:sol:unit01:ex1-2-p3|Question 3, 4 >]]</btn></text>