Część rzeczywista kwadratu liczby zespolonej
: 22 lis 2015, o 17:02
Czy dobrze to rozwiązuję?
\(\displaystyle{ Re \left( Z ^{2} \right) = 0
Z = a + ib}\)
\(\displaystyle{ Z ^{2} = \left( a + ib\right) ^{2} = a ^{2} + 2abi - b ^{2} = a ^{2} - b ^{2} + 2abi}\)
\(\displaystyle{ Re \left( Z ^{2} \right) = a ^{2} - b ^{2} = 0}\)
\(\displaystyle{ a = b \vee a = -b}\)
\(\displaystyle{ Re \left( Z ^{2} \right) = 0
Z = a + ib}\)
\(\displaystyle{ Z ^{2} = \left( a + ib\right) ^{2} = a ^{2} + 2abi - b ^{2} = a ^{2} - b ^{2} + 2abi}\)
\(\displaystyle{ Re \left( Z ^{2} \right) = a ^{2} - b ^{2} = 0}\)
\(\displaystyle{ a = b \vee a = -b}\)