Complex arithmetics - review
Task number: 2478
Calculate
a) \((3+2i)+(1-3i)\),
b) \((3+2i)-(1-3i)\),
c) \((3+2i)(1-3i)\),
d) \((3+2i)/(1-3i)\),
e) \((1+i)^{20}\).
Resolution
a) \((3+2i)+(1-3i)=4-i\),
b) \((3+2i)-(1-3i)=2+5i\),
c) \((3+2i)(1-3i)=3+2i-9i+6=9-7i\),
d) \(\frac{3+2i}{1-3i}= \frac{(3+2i)(1+3i)}{(1-3i)(1+3i)}= \frac{-3+11i}{10}\),
e) \((1+i)^{20}=[\sqrt{2}(\cos\frac\pi4+i\sin\pi4)]^{20}= (\sqrt{2})^{20}(\cos 5\pi +i\sin 5\pi)= -1024\).
