If z=√2-i√2 is rotated through an angle 45° in the anticlockwise direction about the origin, then the co-ordinates of its new position are:

Question

If z=√2-i√2 is rotated through an angle 45° in the anticlockwise direction about the origin, then the co-ordinates of its new position are: (A)  (2,0)  (B)  (√2,√2)  (C)  (√2,-√2)  (D)  (√2,0)

Tardigrade Admin · Accepted Answer

z2=zeiπ /4 =(√2-i√2)( cos π /4+i sin π /4) =√2(1-i)((1+i)/√2) =1-i2=1+1=2+0i ∴ Co-ordinate of new position are (2, 0).

Q. If $z = 2 - i 2$ is rotated through an angle $45^{\circ}$ in the anticlockwise direction about the origin, then the co-ordinates of its new position are:

$(2, 0)$

$(2, 2)$

$(2, - 2)$

$(2, 0)$

$(4, 0)$

$z_{2} = z e^{iπ /4}$
$= (2 - i 2) (cos π /4 + i sin π /4)$
$= 2 (1 - i) \frac{( 1 + i )}{2}$
$= 1 - i^{2} = 1 + 1 = 2 + 0 i$
$∴$ Co-ordinate of new position are (2, 0).

Q. If z=2​−i2​ is rotated through an angle 45∘ in the anticlockwise direction about the origin, then the co-ordinates of its new position are:

(2,0)

(2​,2​)

(2​,−2​)

(2​,0)

(4,0)

z2​=zeiπ/4 =(2​−i2​)(cosπ/4+isinπ/4) =2​(1−i)2​(1+i)​ =1−i2=1+1=2+0i ∴ Co-ordinate of new position are (2, 0).

Q. If $z = 2 - i 2$ is rotated through an angle $45^{\circ}$ in the anticlockwise direction about the origin, then the co-ordinates of its new position are:

$(2, 0)$

$(2, 2)$

$(2, - 2)$

$(2, 0)$

$(4, 0)$

$z_{2} = z e^{iπ /4}$
$= (2 - i 2) (cos π /4 + i sin π /4)$
$= 2 (1 - i) \frac{( 1 + i )}{2}$
$= 1 - i^{2} = 1 + 1 = 2 + 0 i$
$∴$ Co-ordinate of new position are (2, 0).