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- Question 1, Exercise 1.1 @math-11-nbf:sol:unit01
- \cdot i \\ =& -i - i +i = -i \end{align} GOOD ====Go to ==== <text align="left"><btn type="success">[[
- Question 2, Exercise 1.1 @math-11-nbf:sol:unit01
- rac{2}{13}-\dfrac{3}{13}i.\\ \end{align} GOOD ====Go to ==== <text align="left"><btn type="primary">[
- Question 3, Exercise 1.1 @math-11-nbf:sol:unit01
- &\dfrac{25+5i}{5}\\ =&5+i. \end{align} GOOD ====Go to ==== <text align="left"><btn type="primary">[
- Question 4, Exercise 1.1 @math-11-nbf:sol:unit01
- 3y+(2x-4y)i=3+10i\end{align} Now do yourself ====Go to ==== <text align="left"><btn type="primary">[
- Question 5, Exercise 1.1 @math-11-nbf:sol:unit01
- .\end{align} Thus we have $z=x+iy=4-i$. GOOD ====Go to ==== <text align="left"><btn type="primary">[
- Question 6, Exercise 1.1 @math-11-nbf:sol:unit01
- \bar{z}=-\dfrac{5 }{2}i-\dfrac{7}{8}$. GOOD ====Go to ==== <text align="left"><btn type="primary">[
- Question 7, Exercise 1.1 @math-11-nbf:sol:unit01
- 3}-\sqrt{-8})(\sqrt{3}+\sqrt{-8})|=11$. GOOD ====Go to ==== <text align="left"><btn type="primary">[
- Question 1, Exercise 1.2 @math-11-nbf:sol:unit01
- iz)&=x\\ \implies Im(iz)&=Re(z)\end{align} ====Go to ==== <text align="left"><btn type="success">[[
- Question 2, Exercise 1.2 @math-11-nbf:sol:unit01
- ify calculations involving complex numbers. ====Go to ==== <text align="left"><btn type="primary">[
- Question 3, Exercise 1.2 @math-11-nbf:sol:unit01
- $. This gives $z$ is real or pure imaginary. ====Go to ==== <text align="left"><btn type="primary">[[
- Question 4, Exercise 1.2 @math-11-nbf:sol:unit01
- |z_2|=\dfrac{16}{\sqrt{13}}\end{align} GOOD ====Go to ==== <text align="left"><btn type="primary">[[
- Question 5, Exercise 1.2 @math-11-nbf:sol:unit01
- =&4Re(z_1)Re(z_2)+4Im(z_1)Im(z_2).\end{align} ====Go to ==== <text align="left"><btn type="primary">[[
- Question 6, Exercise 1.2 @math-11-nbf:sol:unit01
- \\ &=\dfrac{-3\pm i\sqrt{3}}{2} \end{align} ====Go to ==== <text align="left"><btn type="primary">[[
- Question 7, Exercise 1.2 @math-11-nbf:sol:unit01
- es us $$\sqrt{2} |z| \geq |Re(z)|+|Im(z)|.$$ ====Go to ==== <text align="left"><btn type="primary">[[
- Question 8, Exercise 1.2 @math-11-nbf:sol:unit01
- ities $$-3\leq y \leq 2,$$ as required. GOOD ====Go to ==== <text align="left"><btn type="primary">[[