wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

If 5+12i+512i5+12i512i=a+ib, b<0, then the value of a2b is

Open in App
Solution

Given : 5+12i+512i5+12i512i=a+ib
5+12i+512i5+12i512i=(5+12i+512i)2(5+12i)(512i)=5+12i+512i+2(5+12i)(512i)24i

We know that,
a+ib=±[12(a2+b2+a)+i12(a2+b2a)]5+12i=±(3+2i)
Similarly,
512i=±(32i)a+ib=10±2(3+2i)(32i)24ia+ib=10±2624ia+ib=3i2 and a+ib=2i3
But as given in question b<0
Hence a=0, b=32
So, value of a2b=3

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
Join BYJU'S Learning Program
CrossIcon