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- Question 1, Exercise 1.1
- Question 2 & 3, Exercise 1.1
- Question 4, Exercise 1.1
- Question 5, Exercise 1.1
- Question 6, Exercise 1.1
- Question 7, Exercise 1.1
- Question 8, Exercise 1.1
- Question 9 & 10, Exercise 1.1
- Question 11, Exercise 1.1
- Question 1, Exercise 1.2
- Question 2, Exercise 1.2
- Question 3 & 4, Exercise 1.2
- Question 5, Exercise 1.2
- Question 6, Exercise 1.2
- Question 7, Exercise 1.2
- Question 8, Exercise 1.2
- Question 9, Exercise 1.2
- Question 1, Exercise 1.3
- Question 2, Exercise 1.3
- Question 3 & 4, Exercise 1.3
- Question 5, Exercise 1.3
- Question 6, Exercise 1.3
- Question 1, Review Exercise 1
- Question 2 & 3, Review Exercise 1
- Question 4 & 5, Review Exercise 1
- Question 6, 7 & 8, Review Exercise 1
Fulltext results:
- Question 7, Exercise 1.2
- ====== Question 7, Exercise 1.2 ====== Solutions of Question 7 of Exercise 1.2 of Unit 01: Complex Numbers. This is unit of... k Board (KPTB or KPTBB) Peshawar, Pakistan. =====Question 7(i)===== Separate into real and imaginary parts ... {4}{29}$\\ Imaginary part $=\dfrac{19}{29}$ =====Question 7(ii)===== Separate into real and imaginary parts
- Question 8, Exercise 1.2
- ====== Question 8, Exercise 1.2 ====== Solutions of Question 8 of Exercise 1.2 of Unit 01: Complex Numbers. This is unit of... k Board (KPTB or KPTBB) Peshawar, Pakistan. =====Question 8(i)===== Show that $z+\overline{z}=2\operatorna... operatorname{Re}\left( z \right)\end{align} =====Question 8(ii)===== Show that $z-\overline{z}=2i\operator
- Question 2 & 3, Review Exercise 1
- ====== Question 2 & 3, Review Exercise 1 ====== Solutions of Question 2 & 3 of Review Exercise 1 of Unit 01: Complex Number... k Board (KPTB or KPTBB) Peshawar, Pakistan. =====Question 2===== Show that ${{i}^{n}}+{{i}^{n+1}}+{{i}^{n+2... i\left( 0 \right)\\ &=0=R.H.S.\end{align} =====Question 3(i)===== Express the complex number $\left( 1+3i
- Question 2 & 3, Exercise 1.1
- ====== Question 2 & 3, Exercise 1.1 ====== Solutions of Question 2 & 3 of Exercise 1.1 of Unit 01: Complex Numbers. This is... k Board (KPTB or KPTBB) Peshawar, Pakistan. =====Question 2===== Prove that ${{i}^{107}}+{{i}^{112}}+{{i}^{... \\ &=-i+1-1+i\\ &=0=R.H.S.\end{align} GOOD =====Question 3(i)===== Add the complex numbers $3\left( 1+2i \
- Question 6, Exercise 1.1
- ====== Question 6, Exercise 1.1 ====== Solutions of Question 6 of Exercise 1.1 of Unit 01: Complex Numbers. This is unit of... ok Board (KPTB or KPTBB) Peshawar, Pakistan. =====Question 6(i)===== Perform the indicated division $\dfrac{... \\ &=\dfrac{1}{2}-\dfrac{1}{2}i\end{align} =====Question 6(ii)===== Perform the indicated division $\dfra
- Question 2, Exercise 1.3
- ====== Question 2, Exercise 1.3 ====== Solutions of Question 2 of Exercise 1.3 of Unit 01: Complex Numbers. This is unit of... k Board (KPTB or KPTBB) Peshawar, Pakistan. =====Question 2(i)===== Factorize the polynomial $P(z)$ into li... right]\\ &=(z+2)(z-1+3i)(z-1-3i)\end{align} =====Question 2(ii)===== Factorize the polynomial $P(z)$ into l
- Question 5, Exercise 1.3
- ====== Question 5, Exercise 1.3 ====== Solutions of Question 5 of Exercise 1.3 of Unit 01: Complex Numbers. This is unit of... k Board (KPTB or KPTBB) Peshawar, Pakistan. =====Question 5(i)===== Find the solutions of the equation ${{z... re $-\dfrac{1}{2}\pm\dfrac{\sqrt{11}}{2}i$. =====Question 5(ii)===== Find the solutions of the equation ${{
- Question 1, Exercise 1.1
- ====== Question 1, Exercise 1.1 ====== Solutions of Question 1 of Exercise 1.1 of Unit 01: Complex Numbers. This is unit of... ok Board (KPTB or KPTBB) Peshawar, Pakistan. =====Question 1(i)===== Simplify ${{i}^{9}}+{{i}^{19}}$. GOOD =... -1 \right)\\ &=i-i\\ &=0.\end{align} GOOD =====Question 1(ii)===== Simplify ${{\left( -i \right)}^{23}}$.
- Question 4, Exercise 1.1
- ====== Question 4, Exercise 1.1 ====== Solutions of Question 4 of Exercise 1.1 of Unit 01: Complex Numbers. This is unit of... ok Board (KPTB or KPTBB) Peshawar, Pakistan. =====Question 4(i)===== Subtract the second complex number from... ight)i\\ &=\left( a-2 \right)+bi\end{align} =====Question 4(ii)===== Subtract the second complex number fro
- Question 5, Exercise 1.1
- ====== Question 5, Exercise 1.1 ====== Solutions of Question 5 of Exercise 1.1 of Unit 01: Complex Numbers. This is unit of... ok Board (KPTB or KPTBB) Peshawar, Pakistan. =====Question 5(i)===== Multiply the complex number $8i+11,-7+5... \left( 55-56 \right)i\\ &=-117-i\end{align} =====Question 5(ii)===== Multiply the complex number $3i,2\left
- Question 7, Exercise 1.1
- ====== Question 7, Exercise 1.1 ====== Solutions of Question 7 of Exercise 1.1 of Unit 01: Complex Numbers. This is unit of... ok Board (KPTB or KPTBB) Peshawar, Pakistan. =====Question 7(i)===== If ${{z}_{1}}=1+2i$ and ${{z}_{2}}=2+3i... \ &=\sqrt{9+25}\\ &=\sqrt{34}\end{align} =====Question 7(ii)===== If ${{z}_{1}}=1+2i$ and ${{z}_{2}}=2+3
- Question 8, Exercise 1.1
- ====== Question 8, Exercise 1.1 ====== Solutions of Question 8 of Exercise 1.1 of Unit 01: Complex Numbers. This is unit of... ok Board (KPTB or KPTBB) Peshawar, Pakistan. =====Question 8(i)===== Express the $\dfrac{1-2i}{2+i}+\dfrac{4... &=\dfrac{10}{13}-\dfrac{24i}{13}\end{align} =====Question 8(ii)===== Express the $\dfrac{2+\sqrt{-9}}{-5-\s
- Question 3 & 4, Exercise 1.2
- ====== Question 3 & 4, Exercise 1.2 ====== Solutions of Question 3 & 4 of Exercise 1.2 of Unit 01: Complex Numbers. This is... ok Board (KPTB or KPTBB) Peshawar, Pakistan. =====Question 3===== ${{z}_{1}}=\sqrt{3}+\sqrt{2}i$, ${{z}_{2}}... {3}-1 \right)i\\ L.H.S.&=R.H.S.\end{align} =====Question 4(i)===== Find the additive and multiplicative i
- Question 5, Exercise 1.2
- ====== Question 5, Exercise 1.2 ====== Solutions of Question 5 of Exercise 1.2 of Unit 01: Complex Numbers. This is unit of... k Board (KPTB or KPTBB) Peshawar, Pakistan. =====Question 5(i)===== Let ${{z}_{1}}=2+4i$and ${{z}_{2}}=1-3i... \overline{z_1}+\overline{z_2}$$ as required. =====Question 5(ii)===== Let ${{z}_{1}}=2+3i$ and ${{z}_{2}}=2-
- Question 6, Exercise 1.3
- ====== Question 6, Exercise 1.3 ====== Solutions of Question 6 of Exercise 1.3 of Unit 01: Complex Numbers. This is unit of... k Board (KPTB or KPTBB) Peshawar, Pakistan. =====Question 6(i)===== Find the solutions of the equation ${{z... \pm \dfrac{1}{2}\pm \dfrac{\sqrt{3}}{2}i$$ =====Question 6(ii)===== Find the solutions of the equation ${{