CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

If i=-1, then 4+5-12+i32334+3-12+i32365 is equal to


A

1-i-3

No worries! We‘ve got your back. Try BYJU‘S free classes today!
B

-1+i-3

No worries! We‘ve got your back. Try BYJU‘S free classes today!
C

i3

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D

-i3

No worries! We‘ve got your back. Try BYJU‘S free classes today!
E

1+i3

No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is C

i3


Explanation for correct option:

Given: i=-1and 4+5-12+i32334+3-12+i32365

If in a complex number a+ib, the ratio of a:b=1:3, then it always convert the complex number in ω

-12+i32=ω

So, 4+5-12+i32334+3-12+i32365=4+5ω334+3ω365

=4+5ω333(ω)+3ω363(ω2)=4+5(ω)3111(ω)+3(ω)3121(ω2)=4+51111(ω)+31121(ω2)[ω3=1]=1+3+3(ω)+2(ω)+3(ω2)=1+2(ω)+3(1+ω+ω2)=1+2(ω)+0[1+ω+ω2=0]=1+2-12+i32=1-1+i3

4+5-12+i32334+3-12+i32=i3

Hence option(C) is correct.


flag
Suggest Corrections
thumbs-up
1
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Proportion
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon