1. Verify that
\alpha)(\sqrt{2}-i)-i(1-\sqrt{2}i)=-2i
(2,-3)(-2,1)=(-1,8)
)(31) (3-1)(21)
d) (2+3)-(3-6)=1+91
60
2. Show that
a) Re(iz)-Im(2)
b) Im(iz) Re(z)
c)(z+1)^{2}=z^{2}+2z+1
3. Do the following operations and simplify your answer.
a)\frac{1+2i}{3-4i}+\frac{2-i}{5i}
b \frac{5i}{(1-i)(2-i)(3-i)}
(c)(1-i)^{3}
4. Locate the complex numbers z+z, and z-z, as vectors where
b)z_{1}=(-\sqrt{3},1),z_{2}=(\sqrt{3},0)
c)z_{1}=(-3,1).z_{2}=(1,4 )
d)a+iba-ib
5. Sketch the following set of points determined by the condition given below:
a)|z-1+i|=1
b) z+13
c) 2-424
6. Using properties of conjugate and modulus, show that
a)\overline{z+3i}=z-3ib)\overline{E}=-i\overline{z}
c)\overline{(2+i)^{2}}=3-4
7. Show that (-1+1)=8(-1-1).
b)\overline{z_{1}z_{2}\cdot\cdot\cdot z_{n}}=\overline{z_{1}}\overline{z_{2}}\cdot\cdot\cdot\overline{z_{n}}
8. Using mathematical induction, show that (when n = 2, 3)
a)\overline{z_{1}+z_{2}+\cdot\cdot\cdot+z_{n}}=\overline{z_{1}}+\overline{z_{2}}+\cdot\cdot\cdot+\overline{z}
_{n}
b) \overline{z_{1}z_{2}\cdot\cdot\cdot z_{n}}=\overline{z_{1}}\overline{z_{2}}\cdot\cdot\cdot\overline{z_{n}}