Question

一道高中 复数 数学题

设x,y属于R，且[x /(1-i) ] +[y /(1-2i)]=5/(1-3i) ,求x+y的值
要详细步骤

Answer 1

x/(1-i)]+[y/(1-2i)]=[5/(1-3i)]
即
[x(1+i)/(1-i)(1+i)]+[y(1+2i)/(1-2i)(1+2i)]=[5(1+3i)/(1-3i)(1+3i)]
即
5x+5xi+2y+4yi=5+15i
即
(5x+2y)+(5x+4y)i=5+15i
所以得到
5x+2y=5
5x+4y=15

所以
x=-1
y=5
所以x+y=5/2

Answer 2

x/(1-i)]+[y/(1-2i)]=[5/(1-3i)]
即
[x(1+i)/(1-i)(1+i)]+[y(1+2i)/(1-2i)(1+2i)]=[5(1+3i)/(1-3i)(1+3i)]
即
5x+5xi+2y+4yi=5+15i
即
(5x+2y)+(5x+4y)i=5+15i
所以得到
5x+2y=5
5x+4y=15

所以
x=-1
y=5

Answer 3

x=-5/2
y=5
所以x+y=5/2