QJEEM16Ma0e8c: JEE Main 2016 Mathematics - Class 11 JEEM16Ma0e8c Solution: The point represented by 2 + i in the Argand plane moves 1 unit …

Question

Verified Solution • 2025–26 Session moderate

The point represented by 2 + i in the Argand plane moves 1 unit eastwards, then 2 units northwards and finally from there

2\sqrt 2

units in the south-westwardsdirection. Then its new position in the Argand plane is at the point represented by :

Accepted Answer

Here,

z

-

(3 + 3i) =

2\sqrt 2

(cos(

-

135^o) + i sin (

-

135^o))

=

2\sqrt 2

(

-

{1 \over {\sqrt 2 }}

-

{i \over {\sqrt 2 }}

)

=

-

2

-

2i

\Rightarrow

z = 3 + 3 i

-

2

-

2 i = 1 + i

Note :

Polar form of a complex number :

z = r (cos

\theta

+ i sin

\theta

)

Here r = modulus of z and

\theta

argument of z.

Step-by-Step Verified Solution