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

# Assertion :If z=i+2i2+3i3+.............+32i32, then z,Â¯Â¯Â¯z,z & Â¯Â¯Â¯z forms the vertices of square on argand plane. Reason: z,Â¯Â¯Â¯z,z,Â¯Â¯Â¯z are situated at the same distance from the origin on argand plane.

A
Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
No worries! Weâ€˜ve got your back. Try BYJUâ€˜S free classes today!
B
Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C
Assertion is correct but Reason is incorrect
No worries! Weâ€˜ve got your back. Try BYJUâ€˜S free classes today!
D
Assertion is incorrect but Reason is correct
No worries! Weâ€˜ve got your back. Try BYJUâ€˜S free classes today!
Open in App
Solution

## The correct option is B Both Assertion and Reason are correct but Reason is not the correct explanation for Assertionz=i+2i2+3i3+...32i32And iz=i2+2i3+3i4+...31i32+32i33Now z(1−i)=i+i2+i3+..i32−32i33z(1−i)=i(i32−1)i−1−32i32.iz(1−i)=−32.i since i32=1Or z=−32i1−i=−16.(i)(1+i)=−16(i−1)=16(1−i)=16√2[1−i√2]=16√2.e−iπ4Hencez=16√2.e−iπ4¯z=16√2.eiπ4.Now both z and ¯z are equidistant from the origin, and origin, z,¯z forms a right angled isosceles triangle.

Suggest Corrections
0
Join BYJU'S Learning Program
Related Videos
Introduction to Limits
MATHEMATICS
Watch in App
Explore more
Join BYJU'S Learning Program