165. Given complex numbers $z_{1}=2+3 i, z_{2}=5-7 i$. Find: a) $z_{1}+z_{2}$; b) $z_{1}-z_{2}$; c) $z_{1} z_{2}$.
Solution. a) $z_{1}+z_{2}=(2+3 i)+(5-7 i)=2+3 i+5-7 i=(2+$ $+5)+(3 i-7 i)=7-4 i$

b) $z_{1}-z_{2}=(2+3 i)-(5-7 i)=2+3 i-5+7 i=(2-5)+(3 i+7 i)=$ $=-3+10 i$

c) $z_{1} z_{2}=(2+3 i)(5-7 i)=10-14 i+15 i-21 i^{2}=10-14 i+15 i+$ $+21=(10+21)+(-14 i+15 i)=31+i$, (here it is taken into account that $\left.i^{2}=-1\right)$. 166-173. Perform addition and subtraction of complex numbers: