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

Equation of Circle in Complex Form

If z=4-3i is ...

Question

If $z = 4 - 3 i$ is rotated by $180^{\circ}$ in the clockwise direction about origin and stretched three times of its original length, then the new complex number is

12 + 9 i

No worries! We‘ve got your back. Try BYJU‘S free classes today!

12 - 9 i

No worries! We‘ve got your back. Try BYJU‘S free classes today!

- 12 - 9 i

No worries! We‘ve got your back. Try BYJU‘S free classes today!

- 12 + 9 i

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Open in App

Solution

The correct option is D $- 12 + 9 i$
Given complex number $z = 4 - 3 i$
Let the new rotated complex number be $z_{1}$ , then
$| z_{1} | = 3 | z |$
Also,
$\frac{z_{1}}{z} = \frac{| z_{1} |}{| z |} e^{- i π} \Rightarrow \frac{z_{1}}{z} = - 3 ∴ z_{1} = - 12 + 9 i$

Suggest Corrections

Similar questions

Q. If the point represented by the complex number

i z

is rotated about the origin through the angle

\frac{π}{2}

in the counter clockwise direction then the complex number representing the new position is

Q. In the Argand plane, the vector

z = 4 - 3 i

is turned in the clockwise sense through 180

^{o}

and stretched three times. The complex number represented by the new vector is

Q. The complex number

3 + 4 i

is rotated about origin by an angle of

\frac{π}{4}

and then stretched 2 times. The complex number corresponding to new position is

In the Argand plane, the vector z=4-3i is turned in the clockwise sense through $180^{o}$ and stretched three times. The complex number represented by the new vector is

Q. If

z = \sqrt{2} - i \sqrt{2}

is rotated through an angle 45° in the anti-clockwise direction about the origin, then the coordinates of its new position are
[Kerala (Engg.) 2005]

Join BYJU'S Learning Program

Explore more

Equation of Circle in Complex Form

Standard XII Mathematics

Join BYJU'S Learning Program

If z=4−3i is rotated by 180∘ in the clockwise direction about origin and stretched three times of its original length, then the new complex number is

The correct option is D −12+9iGiven complex number z=4−3i Let the new rotated complex number be z1, then |z1|=3|z| Also, z1z=|z1||z|e−iπ⇒z1z=−3∴z1=−12+9i

If $z = 4 - 3 i$ is rotated by $180^{\circ}$ in the clockwise direction about origin and stretched three times of its original length, then the new complex number is

The correct option is D $- 12 + 9 i$
Given complex number $z = 4 - 3 i$
Let the new rotated complex number be $z_{1}$ , then
$| z_{1} | = 3 | z |$
Also,
$\frac{z_{1}}{z} = \frac{| z_{1} |}{| z |} e^{- i π} \Rightarrow \frac{z_{1}}{z} = - 3 ∴ z_{1} = - 12 + 9 i$