Let w 1 be the point obtained by the rotation of z 1 = 5 + 4 i about the origin through a right angle in the anticlockwise direction, and w 2 be the point obtained by the rotation of z 2 = 3 + 5 i about the origin through a right angle in the cloc

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Q.
Let $w_{1}$ be the point obtained by the rotation of $z_{1} = 5 + 4 i$ about the origin through a right angle in the anticlockwise direction, and $w_{2}$ be the point obtained by the rotation of $z_{2} = 3 + 5 i$ about the origin through a right angle in the clockwise direction. Then the principal argument of $w_{1} - w_{2}$ is equal to [2023]

1 $- π + \tan^{- 1} \frac{33}{5}$

2 $π - \tan^{- 1} \frac{33}{5}$

3 $- π + \tan^{- 1} \frac{8}{9}$

4 $π - \tan^{- 1} \frac{8}{9}$

Ans.
(4)

$w_{1} = z_{1} i = (5 + 4 i) i = - 4 + 5 i$

$w_{2} = z_{2} (- i) = (3 + 5 i) (- i) = 5 - 3 i$

$w_{1} - w_{2} = - 9 + 8 i$

$Principal argument = π - \tan^{- 1} (\frac{8}{9})$

Solution

1 $- π + \tan^{- 1} \frac{33}{5}$

2 $π - \tan^{- 1} \frac{33}{5}$

3 $- π + \tan^{- 1} \frac{8}{9}$

4 $π - \tan^{- 1} \frac{8}{9}$

Ans.
(4)

$w_{1} = z_{1} i = (5 + 4 i) i = - 4 + 5 i$

$w_{2} = z_{2} (- i) = (3 + 5 i) (- i) = 5 - 3 i$

$w_{1} - w_{2} = - 9 + 8 i$

$Principal argument = π - \tan^{- 1} (\frac{8}{9})$

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Solution

1 -π+tan-1335

2 π-tan-1335

3 -π+tan-189

4 π-tan-189

Ans. (4) w1=z1i=(5+4i)i=-4+5i w2=z2(-i)=(3+5i)(-i)=5-3i w1-w2=-9+8i Principal argument=π-tan-1(89)

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1 $- π + \tan^{- 1} \frac{33}{5}$

2 $π - \tan^{- 1} \frac{33}{5}$

3 $- π + \tan^{- 1} \frac{8}{9}$

4 $π - \tan^{- 1} \frac{8}{9}$

Ans.
(4)

$w_{1} = z_{1} i = (5 + 4 i) i = - 4 + 5 i$

$w_{2} = z_{2} (- i) = (3 + 5 i) (- i) = 5 - 3 i$

$w_{1} - w_{2} = - 9 + 8 i$

$Principal argument = π - \tan^{- 1} (\frac{8}{9})$