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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 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 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 6, 7 & 8, Review Exercise 1
- ====== Question 6, 7 & 8, Review Exercise 1 ====== Solutions of Question 6, 7 & 8 of Review Exercise 1 of Unit 01: Complex ... k Board (KPTB or KPTBB) Peshawar, Pakistan. =====Question 6===== Find conjugate of $\dfrac{1}{3+4i}$.\\ ===... s $$\bar{z}=\dfrac{3}{25}+\dfrac{4}{25}i.$$ =====Question 7===== Find the multiplicative inverse of $\dfrac
- Question 4 & 5, Review Exercise 1
- ====== Question 4 & 5, Review Exercise 1 ====== Solutions of Question 4 & 5 of Review Exercise 1 of Unit 01: Complex Number... k Board (KPTB or KPTBB) Peshawar, Pakistan. =====Question 4===== If ${{z}_{1}}=2-i$, ${{z}_{2}}=1+i,$ find ... }^{2}}+{{1}^{2}}}\\ &=\sqrt{2}\end{align} =====Question 5===== Find the modulus of $\dfrac{1+i}{1-i}-\dfr
- Question 1, Review Exercise 1
- ====== Question 1, Review Exercise 1 ====== Solutions of Question 1 of Review Exercise 1 of Unit 01: Complex Numbers. This ... Board (KPTB or KPTBB) Peshawar, Pakistan. ===== Question 1 ===== Chose the correct option. <panel> i. ... align="right"><btn type="success">[[math-11-kpk:sol:unit01:review-ex-1-p2|Question 2 & 3 >]]</btn></text>
- 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 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$$ =====Question 6(ii)===== Find the solutions of the equation ${{
- Question 5, Exercise 1.3
- ====== Question 5, Exercise 1.3 ====== Solutions of Question 5 of Exercise 1.3 of Unit 01: Complex Numbers. This is unit of... k Board (KPTB or KPTBB) Peshawar, Pakistan. =====Question 5(i)===== Find the solutions of the equation ${{z... re $-\dfrac{1}{2}\pm\dfrac{\sqrt{11}}{2}i$. =====Question 5(ii)===== Find the solutions of the equation ${{
- Question 3 & 4, Exercise 1.3
- ====== Question 3 & 4, Exercise 1.3 ====== Solutions of Question 3 & 4 of Exercise 1.3 of Unit 01: Complex Numbers. This is... ok Board (KPTB or KPTBB) Peshawar, Pakistan. =====Question 3===== Show that each ${{z}_{1}}=-1+i$ and ${{z}_... implies $z_2=-1-i$ satisfied the equation. =====Question 4===== Determine weather $1+2i$ is a solution of
- Question 2, Exercise 1.3
- ====== Question 2, Exercise 1.3 ====== Solutions of Question 2 of Exercise 1.3 of Unit 01: Complex Numbers. This is unit of... k Board (KPTB or KPTBB) Peshawar, Pakistan. =====Question 2(i)===== Factorize the polynomial $P(z)$ into li... right]\\ &=(z+2)(z-1+3i)(z-1-3i)\end{align} =====Question 2(ii)===== Factorize the polynomial $P(z)$ into l
- Question 9, Exercise 1.2
- ====== Question 9, Exercise 1.2 ====== Solutions of Question 9 of Exercise 1.2 of Unit 01: Complex Numbers. This is unit of... Board (KPTB or KPTBB) Peshawar, Pakistan. =====Question 9(i)===== If $z=3+2i,$ then verify that $-|z|\leq... ame{Re}\left( z \right)\leq |z|\end{align} =====Question 9(ii)===== If $z=3+2i,$ then verify that $-|z|\le
- Question 1, Exercise 1.3
- ====== Question 1, Exercise 1.3 ====== Solutions of Question 1 of Exercise 1.3 of Unit 01: Complex Numbers. This is unit of... k Board (KPTB or KPTBB) Peshawar, Pakistan. =====Question 1(i)===== Solve the simultaneous linear equation ... -i\end{align} Hence $$z=4-i, \quad w=1-i.$$ =====Question 1(ii)===== Solve the simultaneous linear equation
- 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 $z-\overline{z}=2i\operator
- Question 7, Exercise 1.2
- ====== Question 7, Exercise 1.2 ====== Solutions of Question 7 of Exercise 1.2 of Unit 01: Complex Numbers. This is unit of... k Board (KPTB or KPTBB) Peshawar, Pakistan. =====Question 7(i)===== Separate into real and imaginary parts ... {4}{29}$\\ Imaginary part $=\dfrac{19}{29}$ =====Question 7(ii)===== Separate into real and imaginary parts
- Question 6, Exercise 1.2
- ====== Question 6, Exercise 1.2 ====== Solutions of Question 6 of Exercise 1.2 of Unit 01: Complex Numbers. This is unit of... k Board (KPTB or KPTBB) Peshawar, Pakistan. =====Question 6(i)===== Show that for all complex numbers ${{z}... =|{{z}_{1}}||{{z}_{2}}|\end{align} proved. =====Question 6(ii)===== Show that for all complex numbers ${{z