Question

Решить комплексное число подробно.

Answer 1

$frac{5-i sqrt{2} }{1+i sqrt{2} }= frac{(5-i sqrt{2})(1-i sqrt{2})}{(1+i sqrt{2})(1-i sqrt{2}) }= frac{5-i sqrt{2}-i5sqrt{2}+i ^{2}cdot2 }{(1)^{2}-i^{2} (sqrt{2})^{2}) }= frac{5-i6sqrt{2}-1cdot2 }{ 1-(-1) cdot 2 }= \ = frac{3-i6sqrt{2}}{ 3 }=1-icdot2 sqrt{2}$