A complex number z 1 is rotated through an angle of - clockwise- about the origin to reach Z 2- Then z 2- z 1 equals toA- 2 e-i -B- ei -C- e-i -D- 2 ei -

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Pure Rotation about an Axis

A complex num...

Question

A complex number z₁ is rotated through an angle of $θ$ clockwise, about the origin to reach $z_{2}$ .Then $\frac{z_{2}}{z_{1}}$ equals to

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Solution

The correct option is C

When we rotate through an angle of θ clockwise, the multiplication factor is $e^{- i θ}$

$\Rightarrow$ $\frac{z_{1}}{z_{2}}$ = $e^{- i θ}$

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A complex number z1 is rotated through an angle of θ clockwise, about the origin to reach z2.Then z2z1 equals to

The correct option is C When we rotate through an angle of θ clockwise, the multiplication factor is e−iθ ⇒ z1z2 = e−iθ

A complex number z₁ is rotated through an angle of $θ$ clockwise, about the origin to reach $z_{2}$ .Then $\frac{z_{2}}{z_{1}}$ equals to

The correct option is C

When we rotate through an angle of θ clockwise, the multiplication factor is $e^{- i θ}$

$\Rightarrow$ $\frac{z_{1}}{z_{2}}$ = $e^{- i θ}$