CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon


Question

which among the following is a root of the equation x62x3+2=0 is :


A
21/6eπi/12
loader
B
21/2eπi/12 
loader
C
6eπi/12
loader
D
eπi/12
loader

Solution

The correct option is A 21/6eπi/12
Let x3=z
Hence the equation we get z22z+2=0
z=x3=1+i or z=x3=1i
By using formula, we get
x3=2(1+i2)
x=216ei(2kπ+π4)3,   k 0, 1, 2

Hence roots of the x3=1+i is
216eiπ12, 216ei9π12,216ei17π12
Similarly for x3=1i
 Here θ=π4
and  roots are
216eiπ12, 216ei7π12,216ei15π12
Hence 6 roots of the equation are 
216eiπ12, 216ei9π12,216ei17π12,216eiπ12, 216ei7π12,216ei15π12

 

Mathematics

Suggest Corrections
thumbs-up
 
0


similar_icon
Similar questions
View More


similar_icon
People also searched for
View More



footer-image