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- Question 1, Exercise 1.3
- hat \begin{align}z-4w&=3i …(i)\\ 2z+3w&=11-5i …(ii)\end{align} Multiply $2$ by (i), we get\\ \begin{... 2z-8w&=6i …(iii)\end{align} Subtract (iii) from (ii), we get\\ \[\begin{array}{cccc} 2z&-8w&=6i \\ ... n} Hence $$z=4-i, \quad w=1-i.$$ =====Question 1(ii)===== Solve the simultaneous linear equation with... en that \begin{align}z+w&=3i …(i)\\ 2z+3w&=2 …(ii)\end{align} Multiply $2$ by (i), we get\\ \begin{
- Question 1, Exercise 1.2
- \begin{align} z_2+z_1&=(1-i)+(2+i)\\ &=3 \ldots (ii)\end{align} From (i) and (ii), we get required result. Now, we prove commutative property under mult
- Question 1, Exercise 1.1
- \\ &=i-i\\ &=0.\end{align} GOOD =====Question 1(ii)===== Simplify ${{\left( -i \right)}^{23}}$. GOOD
- Question 2 & 3, Exercise 1.1
- 6 \right)i\\ &=1+12i\end{align} =====Question 3(ii)===== Add the complex numbers $\dfrac{1}{2}-\dfra
- Question 4, Exercise 1.1
- \left( a-2 \right)+bi\end{align} =====Question 4(ii)===== Subtract the second complex number from fir
- Question 5, Exercise 1.1
- 6 \right)i\\ &=-117-i\end{align} =====Question 5(ii)===== Multiply the complex number $3i,2\left( 1-i
- Question 6, Exercise 1.1
- {1}{2}-\dfrac{1}{2}i\end{align} =====Question 6(ii)===== Perform the indicated division $\dfrac{1}{
- Question 7, Exercise 1.1
- +25}\\ &=\sqrt{34}\end{align} =====Question 7(ii)===== If ${{z}_{1}}=1+2i$ and ${{z}_{2}}=2+3i$, e
- Question 8, Exercise 1.1
- }{13}-\dfrac{24i}{13}\end{align} =====Question 8(ii)===== Express the $\dfrac{2+\sqrt{-9}}{-5-\sqrt{-
- Question 11, Exercise 1.1
- 1}}}} \right)=\dfrac{-2}{5}.$$ =====Question 11(ii)===== Let $z_1=2-i$. Find ${\rm Im}\left( \dfrac{
- Question 3 & 4, Exercise 1.2
- $\dfrac{5}{29}-\dfrac{2}{29}i$. =====Question 4(ii)===== Find the additive and multiplicative inver
- Question 5, Exercise 1.2
- _1}+\overline{z_2}$$ as required. =====Question 5(ii)===== Let ${{z}_{1}}=2+3i$ and ${{z}_{2}}=2-3i$.
- Question 6, Exercise 1.2
- ||{{z}_{2}}|\end{align} proved. =====Question 6(ii)===== Show that for all complex numbers ${{z}_{1}
- Question 7, Exercise 1.2
- Imaginary part $=\dfrac{19}{29}$ =====Question 7(ii)===== Separate into real and imaginary parts $\df
- Question 8, Exercise 1.2
- e{Re}\left( z \right)\end{align} =====Question 8(ii)===== Show that $z-\overline{z}=2i\operatorname{