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- Question 1, Exercise 1.1
- estion 1(i)===== Simplify ${{i}^{9}}+{{i}^{19}}$. GOOD ====Solution==== \begin{align}{{i}^{9}}+{{i}^{1... i\cdot\left( -1 \right)\\ &=i-i\\ &=0.\end{align} GOOD =====Question 1(ii)===== Simplify ${{\left( -i \right)}^{23}}$. GOOD ====Solution==== \begin{align}{{\left( -i \righ... 1}}\\ &=-i\cdot\left( -1 \right)\\ &=i\end{align} GOOD =====Question 1(iii)===== Simplify ${{\left( -1
- Question 2 & 3, Exercise 1.1
- i}^{107}}+{{i}^{112}}+{{i}^{122}}+{{i}^{153}}=0$. GOOD ====Solution==== \begin{align}L.H.S.&={{i}^{107... ght)}^{76}}\\ &=-i+1-1+i\\ &=0=R.H.S.\end{align} GOOD =====Question 3(i)===== Add the complex number... right)+\left( 1+\sqrt{2} \right)i\end{align} ====Go to ==== |<text align="left"><btn type="primary">
- Question 7, Exercise 1.1
- {169}}\\ &=\dfrac{\sqrt{65}}{13}\end{align} ==== Go to==== <text align="left"><btn type="primary">[[m
- Question 8, Exercise 1.1
- \\ &=\dfrac{6}{25}+\dfrac{8i}{25}\end{align} ====Go to==== <text align="left"><btn type="primary">[[m
- Question 9 & 10, Exercise 1.1
- \ &=-\left( 2i-2 \right)\\ &=2-2i\end{align} ====Go to==== <text align="left"><btn type="primary">[[m
- Question 11, Exercise 1.1
- left(\dfrac{1}{z_1\overline{z_1}}\right)=0.$$ ====Go to==== <text align="left"><btn type="primary">[[m
- Question 1, Exercise 1.2
- } From (1) and (2), we get required result. === Go to=== <text align="right"><btn type="success">[[m
- Question 2, Exercise 1.2
- rom (3) and (4), we get the required result. ==== Go To ==== <text align="left"><btn type="primary">[[
- Question 3 & 4, Exercise 1.2
- (7,-9)$ is $\dfrac{7}{130}+\dfrac{9}{130}i$. ==== Go To ==== <text align="left"><btn type="primary">[[
- Question 5, Exercise 1.2
- overline{{{z}_{1}}}}{\overline{{{z}_{2}}}}.$$ ====Go to==== <text align="left"><btn type="primary">[[m
- Question 6, Exercise 1.2
- {{z}_{2}}|}{|{{z}_{2}}|}=R.H.S.\end{align} ==== Go To ==== <text align="left"><btn type="primary">[[
- Question 7, Exercise 1.2
- {169}$\\ Imaginary part $=\dfrac{308}{169}$ ==== Go To ==== <text align="left"><btn type="primary">[[
- Question 8, Exercise 1.2
- using (2).} \end{align} This was required. ==== Go To ==== <text align="left"><btn type="primary">[[
- Question 9, Exercise 1.2
- s &-|z|\leq {\rm Im}(z) \leq |z| \end{align} ==== Go To ==== <text align="left"><btn type="primary">[[
- Question 1, Exercise 1.3
- -2i\end{align} Hence $$z=1, \quad w=3-2i.$$ ====Go to ==== <text align="left"><btn type="success">[[