The point represented by 2 + i in the Argand plane moves 1 unit eastwards, then 2 units no…

Question

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(-135o) + i sin (- 135o))

= $$2\sqrt 2 $$ (- $${1 \over {\sqrt 2 }}$$ - ${i \over {\sqrt 2 }}$)

=$-$2$-$2i$ \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 $

Solutions · 1