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- Question 1, Exercise 1.1
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- \cdot i \\
=& -i - i +i = -i
\end{align}
GOOD
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- Question 2, Exercise 1.1
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- rac{2}{13}-\dfrac{3}{13}i.\\
\end{align}
GOOD
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- Question 3, Exercise 1.1
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- &\dfrac{25+5i}{5}\\
=&5+i.
\end{align}
GOOD
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- Question 4, Exercise 1.1
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- 3y+(2x-4y)i=3+10i\end{align}
Now do yourself
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- Question 5, Exercise 1.1
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- .\end{align}
Thus we have $z=x+iy=4-i$.
GOOD
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- Question 6, Exercise 1.1
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- \bar{z}=-\dfrac{5 }{2}i-\dfrac{7}{8}$.
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- Question 7, Exercise 1.1
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- 3}-\sqrt{-8})(\sqrt{3}+\sqrt{-8})|=11$.
GOOD
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- Question 1, Exercise 1.2
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- iz)&=x\\
\implies Im(iz)&=Re(z)\end{align}
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- Question 2, Exercise 1.2
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- ify calculations involving complex numbers.
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- Question 3, Exercise 1.2
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- $.
This gives $z$ is real or pure imaginary.
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- Question 4, Exercise 1.2
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- |z_2|=\dfrac{16}{\sqrt{13}}\end{align}
GOOD
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- Question 5, Exercise 1.2
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- =&4Re(z_1)Re(z_2)+4Im(z_1)Im(z_2).\end{align}
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- Question 6, Exercise 1.2
- 1 Hits, Last modified:
- \\
&=\dfrac{-3\pm i\sqrt{3}}{2}
\end{align}
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- Question 7, Exercise 1.2
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- es us
$$\sqrt{2} |z| \geq |Re(z)|+|Im(z)|.$$
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- Question 8, Exercise 1.2
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- ities
$$-3\leq y \leq 2,$$
as required. GOOD
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- Question 9, Exercise 1.2
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- Question 10, Exercise 1.2
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- Question 1, Exercise 1.3
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- Question 2, Exercise 1.3
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- Question 3, Exercise 1.3
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- Question 4, Exercise 1.3
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- Question 1, Exercise 1.4
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- Question 2, Exercise 1.4
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- Question 3, Exercise 1.4
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- Question 4, Exercise 1.4
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- Question 5, Exercise 1.4
- 1 Hits, Last modified:
- Question 6(i-ix), Exercise 1.4
- 1 Hits, Last modified:
- Question 6(x-xvii), Exercise 1.4
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- Question 7, Exercise 1.4
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- Question 8, Exercise 1.4
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- Question 9, Exercise 1.4
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- Question 10, Exercise 1.4
- 1 Hits, Last modified:
- Question 1, Review Exercise
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- Question 2, Review Exercise
- 1 Hits, Last modified:
- Question 3, Review Exercise
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- Question 4, Review Exercise
- 1 Hits, Last modified:
- Question 5, Review Exercise
- 1 Hits, Last modified:
- Question 6, Review Exercise
- 1 Hits, Last modified:
- Question 7, Review Exercise
- 1 Hits, Last modified:
- Question 8, Review Exercise
- 1 Hits, Last modified: