The point represented by 2 + i in the Argand | vedclass

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Question

(A) The initial position is $z_0 = 2 + i$,which corresponds to the point $(2, 1)$ in the Argand plane.Moving $1 \, 	ext{unit}$ eastwards changes the

Vedclass · Accepted Answer

$1+i$

Vedclass · Answer

(A) The initial position is $z_0 = 2 + i$,which corresponds to the point $(2, 1)$ in the Argand plane.Moving $1 \, 	ext{unit}$ eastwards changes the position to $(2+1, 1) = (3, 1)$.Moving $2 \, 	ext{units}$ northwards changes the position to $(3, 1+2) = (3, 3)$.Finally,moving $2\sqrt{2} \, 	ext{units}$ in the south-westwards direction means moving $2 \, 	ext{units}$ west and $2 \, 	ext{units}$ south (since the displacement vector is $(-2\sqrt{2} \cos(45^{\circ}), -2\sqrt{2} \sin(45^{\circ})) = (-2, -2)$).The final position is $(3-2, 3-2) = (1, 1)$.This corresponds to the complex number $1 + i$.

The point represented by $2 + i$ in the Argand plane moves $1 \, \text{unit}$ eastwards,then $2 \, \text{units}$ northwards and finally from there $2\sqrt{2} \, \text{units}$ in the south-westwards direction. Then its new position in the Argand plane is at the point represented by

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