You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard V

Mathematics

Raw Data and Collection of Data

The multiplic...

Question

The multiplication of a non-zero complex number by i rotates it through ____________ in the anti-clockwise direction.

Open in App

Solution

Let z = x + iy then iz = ix + i²y
i.e iz = ix – y
i.e iz = – y + ix
$\tan θ_{1} for z = x + i y, \tan θ_{1} = \frac{y}{x} \tan θ_{2} for i z = i x - y, \tan θ_{2} = \frac{x}{- y} Since \tan θ_{1} \times \tan θ_{2} = \frac{y}{x} \times \frac{x}{- y} = - 1$
i.e iz is rotated by 90°.

Suggest Corrections

Similar questions

Q. A force of 5 N acts on the top end of the blade of a stationary fan to rotate it anti-clockwise. At the same time, another force of 10 N acts on the middle point of the same blade to rotate it clockwise. In which direction the fan will rotate?

Q. Rotating a figure through

90^{o}

in clockwise direction is the same as rotating it through

Q. The point

A (4, 1)

undergoes following transformations successively :
(i) reflection about line

y = x

(ii) translation through a distance of

3

units in the positive direction of

x

-axis
(iii) rotation through an angle

105^{\circ}

in anti-clockwise direction about origin

O

.
Then the final position of point

A

Q. A line joining two points

A (2, 0)

and

B (3, 1)

is rotated about

A

in anti-clockwise direction through an angle

15^{0}

. If goes to

C

in the new position, then the coordinates of

C

are

If a line is making an angle of $30^{\circ}$ measured in anti-clockwise direction with the horizontal, what will be the angle formed by its image in a vertical line measured in anti-clockwise direction with the horizontal?

Join BYJU'S Learning Program

The multiplication of a non-zero complex number by i rotates it through ____________ in the anti-clockwise direction.

Let z = x + iy then iz = ix + i2y i.e iz = ix – y i.e iz = – y + ix tan θ1 for z=x+iy, tan θ1=yxtan θ2 for iz=ix-y, tan θ2=x-ySince tan θ1×tan θ2=yx×x-y=-1 i.e iz is rotated by 90°.

Let z = x + iy then iz = ix + i²y
i.e iz = ix – y
i.e iz = – y + ix
$\tan θ_{1} for z = x + i y, \tan θ_{1} = \frac{y}{x} \tan θ_{2} for i z = i x - y, \tan θ_{2} = \frac{x}{- y} Since \tan θ_{1} \times \tan θ_{2} = \frac{y}{x} \times \frac{x}{- y} = - 1$
i.e iz is rotated by 90°.