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- Question 5, Exercise 10.1 @fsc-part1-kpk:sol:unit10
- \left( \alpha +\beta \right)$. ====Solution==== Given: $\tan\alpha =\dfrac{3}{4}$. As $\tan\alpha$ is... arrow \quad \sin\alpha &= \frac{3}{5}\end{align} Given: $\sec \beta =\dfrac{13}{5}.$ As \begin{align... \left( \alpha +\beta \right)$. ====Solution==== Given: $\tan\alpha =\dfrac{3}{4}$. As $\tan\alpha$ is... arrow \quad \sin\alpha &= \frac{3}{5}\end{align} Given: $\sec \beta =\dfrac{13}{5}.$ As \begin{align
- Question 3, Exercise 10.1 @fsc-part1-kpk:sol:unit10
- actly $\cos \left( u+v \right)$ ====Solution==== Given $\sin u=\dfrac{3}{5},$ $0\le u\le \dfrac{\pi }... actly $\tan \left( u-v \right)$ ====Solution==== Given \begin{align}\sin u&=\dfrac{3}{5},\,\,\,\, 0\l... actly $\sin \left( u-v \right)$ ====Solution==== Given \begin{align}\sin u&=\dfrac{3}{5},\,\,\,\, 0\l... actly $\cos \left( u+v \right)$ ====Solution==== Given $\sin u=\dfrac{3}{5},$ $0\le u\le \dfrac{\pi }
- Question 5, Exercise 1.2 @fsc-part1-kpk:sol:unit01
- z}_{1}}}+\overline{{{z}_{2}}}$. ====Solution==== Given ${{z}_{1}}=2+4i$ and ${{z}_{2}}=1-3i$. Thus $\ov... {z}_{1}}}\overline{{{z}_{2}}}$. ====Solution==== Given ${{z}_{1}}=2+3i$ and ${{z}_{2}}=2-3i$\\ Thus $\ov... _{1}}}}{\overline{{{z}_{2}}}}$. ====Solution==== Given ${{z}_{1}}=-a-3bi$ and ${{z}_{2}}=2a-3bi$.\\ Thus
- Question 1, Exercise 1.3 @fsc-part1-kpk:sol:unit01
- =3i\\ &2z+3w=11-5i\end{align} ====Solution==== Given that \begin{align}z-4w&=3i …(i)\\ 2z+3w&=11-5i ... n}&z+w=3i\\ &2z+3w=2\end{align} ====Solution==== Given that \begin{align}z+w&=3i …(i)\\ 2z+3w&=2 …(ii... -i\\ &(2-i)z-w=-1+i\end{align} ====Solution==== Given that \begin{align}3z+\left( 2+i \right)w&=11-i
- Question, Exercise 10.1 @fsc-part1-kpk:sol:unit10
- \left( \alpha -\beta \right)$. ====Solution==== Given: $\sin \alpha=-\dfrac{4}{5}$, $\alpha$ is in 3rd ... \left( \alpha +\beta \right)$. ====Solution==== Given: $\sin \alpha=-\dfrac{4}{5}$, $\alpha$ is in 3rd ... \left( \alpha +\beta \right)$ . ====Solution==== Given: $\sin \alpha=-\dfrac{4}{5}$, $\alpha$ is in 3rd
- Question 2, Exercise 10.2 @fsc-part1-kpk:sol:unit10
- ant, then find $\sin 2\theta $. ====Solution==== Given: $\sin \theta =\dfrac{5}{13}$. Using the identit... ant, then find $\cos 2\theta $. ====Solution==== Given: $\sin \theta =\dfrac{5}{13}$. Using the identit... ant, then find $\tan 2\theta $. ====Solution==== Given: $\sin \theta =\dfrac{5}{13}$. Using the identit
- Question 4 and 5, Exercise 10.2 @fsc-part1-kpk:sol:unit10
- find $\sin \dfrac{\theta }{2}$. ====Solution==== Given: $\cos \theta =-\dfrac{3}{7}$ and terminal ray of... exactly $\sin \dfrac{2\pi }{3}$. ====Solution==== Given: $\sin \dfrac{2\pi }{3}$.\\ By using double angle... exactly $\cos \dfrac{2\pi }{3}$. ====Solution==== Given: $\cos \dfrac{2\pi }{3}$ \\ By using double angle
- Question 11, Exercise 1.1 @fsc-part1-kpk:sol:unit01
- {\overline{{{z}_{1}}}} \right)$. ====Solution==== Given $z_1=2-i$ and $z_2=-2+i$, then $\overline{z_1}=2+... \overline{{{z}_{1}}}} \right)$. ====Solution==== Given $z_1=2-i$, then $\overline{z_1}=2+i$. \begin{alig
- Question 3 & 4, Exercise 1.2 @fsc-part1-kpk:sol:unit01
- e of the complex number $5+2i$. ====Solution==== Given $z=5+2i$. Here $a=5$ and $b=2$. Additive inverse... ex number $\left( 7,-9 \right)$. ====Solution==== Given $z=(7,-9)=7-9i$. Here $a=7$ and $b=-9$. Additive
- Question 9, Exercise 1.2 @fsc-part1-kpk:sol:unit01
- e{Re}\left( z \right)\leq |z|$ ====Solution==== Given $z=3+2i$. Then $|z|=\sqrt{9+4}=\sqrt{13}$ and ${\... e{Im}\left( z \right)\leq |z|$ ====Solution==== Given $z=3+2i$. Then $|z|=\sqrt{9+4}=\sqrt{13}$ and ${\
- Question 2, Exercise 1.3 @fsc-part1-kpk:sol:unit01
- ft( z \right)={{z}^{3}}+6z+20$$ ====Solution==== Given: $$p\left( z \right)={{z}^{3}}+6z+20$$ By factor... (z)={{z}^{3}}-2{{z}^{2}}+z-2.$$ ====Solution==== Given: $$P\left( z \right)={{z}^{3}}-2{{z}^{2}}+z-2$$ \
- Question 3 & 4, Exercise 1.3 @fsc-part1-kpk:sol:unit01
- equation ${{z}^{2}}+2z+2=0$\\ ====Solution==== Given: $$z^2+2z_1+2=0\quad \ldots (i)$$ Put the value o... end{align} This implies $z_1=-1+i$ satisfied the given equation.\\ Now put $z_2=-1-i$ in (i) \begin{alig
- Question 3, Exercise 10.2 @fsc-part1-kpk:sol:unit10
- adrant, then find $\sin2\theta$. ====Solution==== Given: $\sin \theta =\dfrac{4}{5}$ Terminal ray of $\t... find $\cos \dfrac{\theta }{2}$. ====Solution==== Given: $\sin \theta =\dfrac{4}{5}$ Terminal ray of $\t
- Question 1, Exercise 1.2 @fsc-part1-kpk:sol:unit01
- .t. addition and multiplication. ====Solution==== Given ${{z}_{1}}=2+i$, ${{z}_{2}}=1-i$. First, we prove
- Question 2, Exercise 1.2 @fsc-part1-kpk:sol:unit01
- t. addition and multiplication. ====Solution==== Given ${{z}_{1}}=-1+i$, ${{z}_{2}}=3-2i$ and ${{z}_{3}}