在复数集中分解因式:

问题描述:

在复数集中分解因式:
(1)x^2+5y^2 (2)2x^2-6x+5

(1)
原式=x²-5i²y²
=(x+√5iy)(x-√5iy)
(2)2x^2-6x+5
=2(x²-3x+5/2)
=2[(x²-3x+9/4)+1/4]
=2[(x+3/2)²-(i/2)²]
=2(x+3/2+i/2)(x+3/2-i/2)