The co-ordinate axes are rotated through an angle of $60^{\circ}$ anti-clockwise. Find the vector corresponding to 1+i in new co-ordinate axes.

(1+i)

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(1+i)

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(1+i)

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(1+i)

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Solution

The correct option is C
(1+i)

Rotating co-ordinate axes through an angle of $θ$ is equivalent to rotating the vector/complex number through an angle of $- θ$ .

$\Rightarrow$ new vector = (1+i) $e^{\frac{- i π}{3}}$

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Similar questions

Co-ordinate axes are rotated through an angle of $45^{\circ}$ in the anti-Clockwise direction. Find the Co-Ordinates of (2,3) in new co-ordinate system.

In the new coordinate system origin is shifted to (h,k) and the axes are rotated through angle of $90^{\circ}$ in the anti-clockwise direction. The new co-ordinates of (x,y) is obtained by the following method.

1) (x + iy) becomes (x + iy) $e^{\frac{- i π}{2}}$

Let it be (x+iy) or (x,y)

2)(x,y) becomes (x - h,y - k)

1) (x + iy) becomes (x + iy) $e^{\frac{- i π}{2}}$

Let it be (x+iy) or (x,y)

2)(x,y) becomes (x - h,y - k)

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The co-ordinate axes are rotated through an angle of 60∘ anti-clockwise. Find the vector corresponding to 1+i in new co-ordinate axes.

The correct option is C (1+i) Rotating co-ordinate axes through an angle of θ is equivalent to rotating the vector/complex number through an angle of −θ . ⇒ new vector = (1+i) e−iπ3

The co-ordinate axes are rotated through an angle of $60^{\circ}$ anti-clockwise. Find the vector corresponding to 1+i in new co-ordinate axes.

The correct option is C
(1+i)

Rotating co-ordinate axes through an angle of $θ$ is equivalent to rotating the vector/complex number through an angle of $- θ$ .

$\Rightarrow$ new vector = (1+i) $e^{\frac{- i π}{3}}$