wiz-icon
MyQuestionIcon
MyQuestionIcon
7
You visited us 7 times! Enjoying our articles? Unlock Full Access!
Question

Let ω be the complex number cos2π3+isin2π3. Then the number of distinct complex numbers z satisfying ∣ ∣ ∣z+1ωω2ωz+ω21ω21z+ω∣ ∣ ∣=0 is equal to

Open in App
Solution

Given that ω=cos2π3+isin2π3
Therefore, 1+ω+ω2=0 & ω3=1
∣ ∣ ∣z+1ωω2ωz+ω21ω21z+ω∣ ∣ ∣=0
R1R1+R2+R3
∣ ∣ ∣z+1+ω+ω2z+1+ω+ω2z+1+ω+ω2ωz+ω21ω21z+ω∣ ∣ ∣=0
z∣ ∣ ∣111ωz+ω21ω21z+ω∣ ∣ ∣=0
z[(z+w2)(z+w)1ω(z+ω)+ω2ω2(z+ω2)]=0
z[z2+z(ω+ω2)z(ω+ω2)]=0
z3=0
Ans: 1

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Integration by Parts
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon