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- Question 7, Exercise 1.2
- 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
- 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
- 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
- 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 2 & 3, Exercise 1.1
- 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
- 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
- +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
- ^{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
- \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
- {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
- 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
- (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>
- Question 3 & 4, Exercise 1.2
- \dfrac{7}{130}+\dfrac{9}{130}i$. ==== Go To ==== <text align="left"><btn type="primary">[[fsc-part1-kpk:sol:unit01:ex1-2-p2|< Question 2]]</btn></text> <text align="right"><btn type="success">[[fsc-part1-kpk:sol:unit01:ex1-2-p4|Question 5 >]]</btn></text>
- Question 2, Exercise 1.3
- )\\ &=(z-2)(z-i)(z+i).\end{align} ====Go To==== <text align="left"><btn type="primary">[[fsc-part1-kpk:sol:unit01:ex1-3-p1 |< Question 1]]</btn></text> <text align="right"><btn type="success">[[fsc-part1-kpk:sol:unit01:ex1-3-p3|Question 3 & 4 >]]</btn></text>
- Question 3 & 4, Exercise 1.3
- \pm 2i\\ z&=1+2i,1-2i\end{align} ====Go To==== <text align="left"><btn type="primary">[[fsc-part1-kpk:sol:unit01:ex1-3-p2 |< Question 2]]</btn></text> <text align="right"><btn type="success">[[fsc-part1-kpk:sol:unit01:ex1-3-p4|Question 5 >]]</btn></text>