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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 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 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 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 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
- 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}$$ as required. =====Question 5(ii)===== Let ${{z}_{1}}=2+3i$ and ${{z}_{2}}=2-
- Question 3 & 4, Exercise 1.2
- ====== Question 3 & 4, Exercise 1.2 ====== Solutions of Question 3 & 4 of Exercise 1.2 of Unit 01: Complex Numbers. This is... ok Board (KPTB or KPTBB) Peshawar, Pakistan. =====Question 3===== ${{z}_{1}}=\sqrt{3}+\sqrt{2}i$, ${{z}_{2}}... {3}-1 \right)i\\ L.H.S.&=R.H.S.\end{align} =====Question 4(i)===== Find the additive and multiplicative i
- Question 2, Exercise 1.2
- ====== Question 2, Exercise 1.2 ====== Solutions of Question 2 of Exercise 1.2 of Unit 01: Complex Numbers. This is unit of... ok Board (KPTB or KPTBB) Peshawar, Pakistan. =====Question 2===== $z_1=-1+i$, $z_2=3-2i$ and ${{z}_{3}}=2-2i... e="primary">[[fsc-part1-kpk:sol:unit01:ex1-2-p1|< Question 1]]</btn></text> <text align="right"><btn type="s
- Question 1, Exercise 1.2
- ====== Question 1, Exercise 1.2 ====== Solutions of Question 1 of Exercise 1.2 of Unit 01: Complex Numbers. This is unit of... k Board (KPTB or KPTBB) Peshawar, Pakistan. =====Question 1===== If ${{z}_{1}}=2+i$and ${{z}_{2}}=1-i$, the... === <text align="right"><btn type="success">[[fsc-part1-kpk:sol:unit01:ex1-2-p2|Question 2 >]]</btn></text>
- Question 11, Exercise 1.1
- ====== Question 11, Exercise 1.1 ====== Solutions of Question 11 of Exercise 1.1 of Unit 01: Complex Numbers. This is unit ... ok Board (KPTB or KPTBB) Peshawar, Pakistan. =====Question 11(i)===== Let ${{z}_{1}}=2-i$, ${{z}_{2}}=-2+i... rline{{{z}_{1}}}} \right)=\dfrac{-2}{5}.$$ =====Question 11(ii)===== Let $z_1=2-i$. Find ${\rm Im}\left( \
- Question 9 & 10, Exercise 1.1
- ====== Question 9 & 10, Exercise 1.1 ====== Solutions of Question 9 & 10 of Exercise 1.1 of Unit 01: Complex Numbers. This ... ok Board (KPTB or KPTBB) Peshawar, Pakistan. =====Question 9===== Find the conjugate of $\dfrac{\left( 3-2... =\dfrac{63}{25}+\dfrac{16}{25}i\end{align} =====Question 10===== Evalute ${{\left[ {{i}^{18}}+{{\left( \
- 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 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