若1+5i3-i=a+bi(a,b∈R,i为虚数单位),则ab=______.-数学

题目简介

若1+5i3-i=a+bi(a,b∈R,i为虚数单位),则ab=______.-数学

题目详情

1+5i
3-i
=a+bi
(a,b∈R,i为虚数单位),则ab=______.
题型:填空题难度:中档来源:扬州模拟

答案

class="stub"1+5i
3-i
=a+bi
(a,b∈R,i为虚数单位),
∴a+bi=
(1+5i)(3+i)
(3-i)(3+i)
=class="stub"-2+16i
10
=-class="stub"1
5
+class="stub"8
5
i,
∴a=-class="stub"1
5
,b=class="stub"8
5

∴ab=-class="stub"8
25

故答案为:-class="stub"8
25

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