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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 5, Exercise 1.3
- ====== Question 5, Exercise 1.3 ====== Solutions of Question 5 of Exercise 1.3 of Unit 01: Complex Numb... awar, Pakistan. =====Question 5(i)===== Find the solutions of the equation ${{z}^{2}}+z+3=0$\\ ====Solution==== ${{z}^{2}}+z+3=0$\\ According to the quadr... 2}i\end{align} =====Question 5(ii)===== Find the solutions of the equation ${{z}^{2}}-1=z$.\\ ====Solu
- Question 6, Exercise 1.3
- ====== Question 6, Exercise 1.3 ====== Solutions of Question 6 of Exercise 1.3 of Unit 01: Complex Numb... awar, Pakistan. =====Question 6(i)===== Find the solutions of the equation ${{z}^{4}}+{{z}^{2}}+1=0$\\ ====Solution==== \begin{align}{{z}^{4}}+{{z}^{2}}+1&=0\\... }}}\end{align} =====Question 6(ii)===== Find the solutions of the equation ${{z}^{3}}=-8$\\ ====Soluti
- Question 7, Exercise 1.2
- ====== Question 7, Exercise 1.2 ====== Solutions of Question 7 of Exercise 1.2 of Unit 01: Complex Numb... eal and imaginary parts $\dfrac{2+3i}{5-2i}$. ====Solution==== \begin{align}&\dfrac{2+3i}{5-2i} \\ =&\... $\dfrac{{{\left( 1+2i \right)}^{2}}}{1-3i}$. ====Solution==== \begin{align}&\dfrac{(1+2i)^2}{1-3i}\\ ... ts $\dfrac{1-i}{{{\left( 1+i \right)}^{2}}}$. ====Solution==== \begin{align}&\dfrac{1-i}{{{\left( 1+i
- Question 8, Exercise 1.2
- ====== Question 8, Exercise 1.2 ====== Solutions of Question 8 of Exercise 1.2 of Unit 01: Complex Numb... rline{z}=2\operatorname{Re}\left( z \right)$. ====Solution==== Assume $z=a+ib$, then $\overline{z}=a-i... line{z}=2i\operatorname{Im}\left( z \right)$. ====Solution==== Assume that $z=a+ib$, then $\overline{z... ratorname{Im}\left( z \right) \right]}^{2}}$. ====Solution==== Suppose $z=a+ib$, then $\overline{z}=a-
- Question 1, Exercise 1.3
- ====== Question 1, Exercise 1.3 ====== Solutions of Question 1 of Exercise 1.3 of Unit 01: Complex Numb... TBB) Peshawar, Pakistan. =====Question 1(i)===== Solve the simultaneous linear equation with complex c... in{align}&z-4w=3i\\ &2z+3w=11-5i\end{align} ====Solution==== Given that \begin{align}z-4w&=3i …(i)... $$z=4-i, \quad w=1-i.$$ =====Question 1(ii)===== Solve the simultaneous linear equation with complex c
- Question 2 & 3, Review Exercise 1
- ====== Question 2 & 3, Review Exercise 1 ====== Solutions of Question 2 & 3 of Review Exercise 1 of Uni... i}^{n+2}}+{{i}^{n+3}}=0$, $\forall n\in N$ \\ ====Solution==== \begin{align}{{i}^{n}}+{{i}^{n+1}}+{{i}... left( 5+7i \right)$ in the form of $x+iy$.\\ ====Solution==== $\left( 1+3i \right)+\left( 5+7i \right... left( 5+7i \right)$ in the form of $x+iy$.\\ ====Solution==== \begin{align}\left( 1+3i \right)-\left(
- Question 2 & 3, Exercise 1.1
- ====== Question 2 & 3, Exercise 1.1 ====== Solutions of Question 2 & 3 of Exercise 1.1 of Unit 01: Comp... 107}}+{{i}^{112}}+{{i}^{122}}+{{i}^{153}}=0$. ====Solution==== \begin{align}L.H.S.&={{i}^{107}}+{{i}^{1... $3\left( 1+2i \right),-2\left( 1-3i \right)$. ====Solution==== \begin{align}& 3\left( 1+2i \right)+-2\l... 2}-\dfrac{2}{3}i,\dfrac{1}{4}-\dfrac{1}{3}i$. ====Solution==== \begin{align}&\left( \dfrac{1}{2}-\dfrac
- Question 6, Exercise 1.1
- ====== Question 6, Exercise 1.1 ====== Solutions of Question 6 of Exercise 1.1 of Unit 01: Complex Numb... i}$ and write the answer in the form $a+ib$. ====Solution==== \begin{align}\dfrac{4+i}{3+5i}&=\dfrac{4... i}$ and write the answer in the form $a+ib$. ====Solution==== \begin{align}\dfrac{1}{-8+i}&=\dfrac{1}{... i}$ and write the answer in the form $a+ib$. ====Solution==== \begin{align}\dfrac{1}{7-3i}&=\dfrac{1}{
- Question 2, Exercise 1.3
- ====== Question 2, Exercise 1.3 ====== Solutions of Question 2 of Exercise 1.3 of Unit 01: Complex Numb... actors. $$P\left( z \right)={{z}^{3}}+6z+20$$ ====Solution==== Given: $$p\left( z \right)={{z}^{3}}+6... $P(z)$ into linear factors. $$P(z)=3z^2+7.$$ ====Solution==== \begin{align} P(z)&=3z^2+7\\ &=\left(\sq... r factors. $$P\left( z \right)={{z}^{2}}+4$$ ====Solution==== \begin{align}P(z)&={{z}^{2}}+4\\ &={{\l
- Question 1, Exercise 1.1
- ====== Question 1, Exercise 1.1 ====== Solutions of Question 1 of Exercise 1.1 of Unit 01: Complex Numb... on 1(i)===== Simplify ${{i}^{9}}+{{i}^{19}}$. ====Solution==== \begin{align}{{i}^{9}}+{{i}^{19}}&=i\cdo... )===== Simplify ${{\left( -i \right)}^{23}}$. ====Solution==== \begin{align}{{\left( -i \right)}^{23}}&... lify ${{\left( -1 \right)}^{\frac{-23}{2}}}$. ====Solution==== \begin{align}{{\left( -1 \right)}^{\frac
- Question 4, Exercise 1.1
- ====== Question 4, Exercise 1.1 ====== Solutions of Question 4 of Exercise 1.1 of Unit 01: Complex Numb... irst $\left( a,0 \right)\left( 2,-b \right)$. ====Solution==== \begin{align}&\left( a,0 \right)-\left( ... {1}{2} \right)\left( 3,\dfrac{1}{2} \right)$. ====Solution==== \begin{align}&\left( -3,\dfrac{1}{2} \ri... t $3\sqrt{3}-5\sqrt{7}i,\sqrt{3}+2\sqrt{7}i$. ====Solution==== \begin{align}&\left(3\sqrt{3}-5\sqrt{7}i
- Question 5, Exercise 1.1
- ====== Question 5, Exercise 1.1 ====== Solutions of Question 5 of Exercise 1.1 of Unit 01: Complex Numb... == Multiply the complex number $8i+11,-7+5i$. ====Solution==== \begin{align}&(8i+11)\times (-7+5i)\\ &=... the complex number $3i,2\left( 1-i \right)$. ====Solution==== \begin{align}&3i\times 2\left( 1-i \righ... ber $\sqrt{2}+\sqrt{3i},2\sqrt{2}-\sqrt{3i}$. ====Solution==== \begin{align}&\left( \sqrt{2}+\sqrt{3}i
- Question 7, Exercise 1.1
- ====== Question 7, Exercise 1.1 ====== Solutions of Question 7 of Exercise 1.1 of Unit 01: Complex Numb... {2}}=2+3i$, evaluate $|{{z}_{1}}+{{z}_{2}}|$. ====Solution==== We know that $z_1=1+2i$ and $z_2=2+3i$, ... _{2}}=2+3i$, evaluate $|{{z}_{1}}{{z}_{2}}|$. ====Solution==== We know that $z_1=1+2i$ and $z_2=2+3i$, ... i$, evaluate $\left|\dfrac{z_1}{z_2}\right|$. ====Solution==== We know that $z_1=1+2i$ and $z_2=2+3i$,
- Question 8, Exercise 1.1
- ====== Question 8, Exercise 1.1 ====== Solutions of Question 8 of Exercise 1.1 of Unit 01: Complex Numb... {4-i}{3+2i}$ in the standard form of $a+ib.$ ====Solution==== \begin{align}&\dfrac{1-2i}{2+i}+\dfrac{4... \sqrt{-16}}$ in the standard form of $a+ib.$ ====Solution==== \begin{align}\dfrac{2+\sqrt{-9}}{-5-\sqr... {2}}}{4+3i}$ in the standard form of $a+ib.$ ====Solution==== \begin{align}\dfrac{\left( 1+i \right)\l
- Question 3 & 4, Exercise 1.2
- ====== Question 3 & 4, Exercise 1.2 ====== Solutions of Question 3 & 4 of Exercise 1.2 of Unit 01: Comp... property w.r.t. addition and multiplication. ====Solution==== ${{z}_{1}}=\sqrt{3}+\sqrt{2}i$ ${{z}_{2... icative inverse of the complex number $5+2i$. ====Solution==== Given $z=5+2i$. Here $a=5$ and $b=2$. ... of the complex number $\left( 7,-9 \right)$. ====Solution==== Given $z=(7,-9)=7-9i$. Here $a=7$ and $b