Khẳng định nào sai ?
\(\left(2-3i\right)+\left(5+i\right)=7-2i\)\(\left(3-4i\right)-\left(1-6i\right)=2\left(1+i\right)\)\(\left(4-3i\right)\left(2+5i\right)=23+14i\)\(\left(2-\sqrt{3}i\right)\left(\overline{1+i}+\sqrt{3}i\right)=5-\sqrt{3}+\left(2+\sqrt{3}\right)i\)Hướng dẫn giải:Ta có:
\(\left(2-3i\right)+\left(5+i\right)=\left(2+5\right)+\left(-3+1\right)i=7-2i\)
\(\left(3-4i\right)-\left(1-6i\right)=\left(3-1\right)+\left(-4+6\right)i=2+2i=2\left(1+i\right)\)
\(\left(4-3i\right)\left(2+5i\right)=8-15i^2-6i+20i=23+14i\) ( chú ý \(i^2=-1\))
\(\left(2-\sqrt{3}i\right)\left(\overline{1+i}+\sqrt{3}i\right)=\left(2-\sqrt{2}i\right)\left(1-i+\sqrt{3}i\right)=\left(2-\sqrt{2}i\right)\left[1+\left(\sqrt{3}-1\right)i\right]\)
\(=2-\sqrt{2}\left(\sqrt{3}-1\right)i^2+\left(2\sqrt{3}-2-\sqrt{2}\right)i\)
\(=2+\sqrt{2}\left(\sqrt{3}-1\right)+\left(2\sqrt{3}-2-\sqrt{2}\right)i\)
\(\ne5-\sqrt{3}+\left(2+\sqrt{3}\right)i\)
