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- Question 6, Exercise 10.2 @fsc-part1-kpk:sol:unit10
- c{\theta }{2}=\dfrac{{{30}^{\circ }}}{2}$, we can find $\cos {{15}^{\circ }}$by using half angle identit... heta }{2}=\dfrac{{{135}^{\circ }}}{2}$, so we can find $\tan {{67.5}^{\circ }}$by using half angle ident... heta }{2}=\dfrac{{{225}^{\circ }}}{2}$, so we can find $sin{{112.5}^{\circ }}$by using half angle identi... theta }{2}=\dfrac{\dfrac{\pi }{4}}{2}$, so we can find $\cos \dfrac{\pi }{8}$by using half angle identit
- Question 5, Exercise 1.3 @fsc-part1-kpk:sol:unit01
- TBB) Peshawar, Pakistan. =====Question 5(i)===== Find the solutions of the equation ${{z}^{2}}+z+3=0$\\... qrt{11}}{2}i\end{align} =====Question 5(ii)===== Find the solutions of the equation ${{z}^{2}}-1=z$.\\ ... sqrt{5}}{2}\end{align} =====Question 5(iii)===== Find the solutions of the equation ${{z}^{2}}-2z+i=0$\... 1-\sqrt{1-i}\end{align} =====Question 5(iv)===== Find the solutions of the equation ${{z}^{2}}+4=0$\\ =
- Question 6, Exercise 1.3 @fsc-part1-kpk:sol:unit01
- TBB) Peshawar, Pakistan. =====Question 6(i)===== Find the solutions of the equation ${{z}^{4}}+{{z}^{2}... frac{1}{2}}}\end{align} =====Question 6(ii)===== Find the solutions of the equation ${{z}^{3}}=-8$\\ ==... $z=-2,1\pm \sqrt{3}i$$ =====Question 6(iii)===== Find the solutions of the equation ${{\left( z-1 \righ... \dfrac{\sqrt{6}i}{2}$$ =====Question 6(iv)===== Find the solutions of the equation ${{z}^{3}}=1$ \\ ==
- Question 3, Exercise 10.2 @fsc-part1-kpk:sol:unit10
- l ray of $\theta$ is in the second quadrant, then find $\sin2\theta$. ====Solution==== Given: $\sin \the... pk-ex10-2-q3.png?nolink |Reference triangle}} We find: $\cos \theta =-\dfrac{3}{5}$. Thus, we have the... l ray of $\theta$ is in the second quadrant, then find $\cos \dfrac{\theta }{2}$. ====Solution==== Given... pk-ex10-2-q3.png?nolink |Reference triangle}} We find: $\cos \theta =-\dfrac{3}{5}$. Thus, we have th
- Question 6, 7 & 8, Review Exercise 1 @fsc-part1-kpk:sol:unit01
- KPTBB) Peshawar, Pakistan. =====Question 6===== Find conjugate of $\dfrac{1}{3+4i}$.\\ ====Solution===... }-\dfrac{4i}{25}\end{align} =====Question 7===== Find the multiplicative inverse of $\dfrac{3i+2}{3-2i}... of $\dfrac{3i+2}{3-2i}=-i$ =====Question 8===== Find the quadrative equation $z+\dfrac{2}{z}=2.$\\ ===
- Question, Exercise 10.1 @fsc-part1-kpk:sol:unit10
- pha $in Quadrant III and $\beta $in Quadrant II, find the exact value of $\sin \left( \alpha -\beta \r... pha $in Quadrant III and $\beta $in Quadrant II, find the exact value of $\cos \left( \alpha +\beta \r... pha $in Quadrant III and $\beta $in Quadrant II, find the exact value of $\tan \left( \alpha +\beta \
- Question 5, Exercise 10.1 @fsc-part1-kpk:sol:unit10
- $\alpha$ nor $\beta$ in the first Quadrant, then find: $\sin \left( \alpha +\beta \right)$. ====Solut... $\alpha$ nor $\beta$ in the first Quadrant, then find: $\cos \left( \alpha +\beta \right)$. ====Solut... $\alpha$ nor $\beta$ in the first Quadrant, then find: $\tan \left( \alpha +\beta \right)$. ====Solut
- Question 2, Exercise 10.2 @fsc-part1-kpk:sol:unit10
- ray of $\theta $ is in the second quadrant, then find $\sin 2\theta $. ====Solution==== Given: $\sin \... ray of $\theta $ is in the second quadrant, then find $\cos 2\theta $. ====Solution==== Given: $\sin \... ray of $\theta $ is in the second quadrant, then find $\tan 2\theta $. ====Solution==== Given: $\sin \
- Unit 1: Complex Numbers (Solutions)
- ve identity for the set of complex numbers. * Find additive inverse and multiplicative inverse of a ... g properties $|z|=|-z|=|\bar{z}=|-\bar{z}|$ * Find real and imaginary parts of complex numbers.
- Question 11, Exercise 1.1 @fsc-part1-kpk:sol:unit01
- (i)===== Let ${{z}_{1}}=2-i$, ${{z}_{2}}=-2+i$. Find ${\rm Re}\left( \dfrac{{{z}_{1}}{{z}_{2}}}{\overl... {5}.$$ =====Question 11(ii)===== Let $z_1=2-i$. Find ${\rm Im}\left( \dfrac{1}{{{z}_{1}}\overline{{{z}
- Question 3 & 4, Exercise 1.2 @fsc-part1-kpk:sol:unit01
- .S.&=R.H.S.\end{align} =====Question 4(i)===== Find the additive and multiplicative inverse of the co... }{29}-\dfrac{2}{29}i$. =====Question 4(ii)===== Find the additive and multiplicative inverse of the co
- Question 4 & 5, Review Exercise 1 @fsc-part1-kpk:sol:unit01
- estion 4===== If ${{z}_{1}}=2-i$,${{z}_{2}}=1+i,$ find $|\dfrac{{{z}_{1}}+{{z}_{2}}+1}{{{z}_{1}}-{{z}_{2... }\\ &=\sqrt{2}\end{align} =====Question 5===== Find the modulus of $\dfrac{1+i}{1-i}-\dfrac{1-i}{1+i}
- Question 1, Exercise 10.2 @fsc-part1-kpk:sol:unit10
- re four parts in Question 1. =====Question1===== Find the value of $\sin 2\theta ,\,\,\cos 2\theta$ and... k-ex10-2-q1.png?nolink |reference triangle}} we find $\sin \theta =\dfrac{1}{\sqrt{26}}$ and $\cos \
- Question 9 & 10, Exercise 1.1 @fsc-part1-kpk:sol:unit01
- r KPTBB) Peshawar, Pakistan. =====Question 9===== Find the conjugate of $\dfrac{\left( 3-2i \right)\le
- Question 4 and 5, Exercise 10.2 @fsc-part1-kpk:sol:unit10
- l ray of $\theta $ is in the third quadrant, then find $\sin \dfrac{\theta }{2}$. ====Solution==== Given