In the argand plane, the complex number y=x is turned in the clockwise sense through 180? and stretched three times. The complex number represented by the new number is

Question

In the argand plane, the complex number y=x is turned in the clockwise sense through 180? and stretched three times. The complex number represented by the new number is (A)  ∴  (B)  ( (-3-y1/4-x1) )(1)=-1  (C)  ⇒  (D)  y1+x1=1

Tardigrade Admin · Accepted Answer

Given, (3/2)ML2 (3/4)ML2 ML2 This complex number lies in IV quadrant. When we rotate this point in 180Â° clockwise, then this point moves in II quadrant. So, new complex number will be R1 R2 Required complex number is Q1 i.e., Q2

Q. In the argand plane, the complex number $y = x$ is turned in the clockwise sense through 180? and stretched three times. The complex number represented by the new number is

$∴$

$(\frac{- 3 - y _{1}}{4 - x _{1}}) (1) = - 1$

$\Rightarrow$

$y_{1} + x_{1} = 1$

Given, $\frac{3}{2} M L^{2}$ $\frac{3}{4} M L^{2}$ $M L^{2}$ This complex number lies in IV quadrant. When we rotate this point in 180° clockwise, then this point moves in II quadrant. So, new complex number will be $R_{1}$ $R_{2}$ Required complex number is $Q_{1}$ i.e., $Q_{2}$

Q. In the argand plane, the complex number y=x is turned in the clockwise sense through 180? and stretched three times. The complex number represented by the new number is

∴

(4−x1​−3−y1​​)(1)=−1

⇒

y1​+x1​=1

Given, 23​ML2 43​ML2 ML2 This complex number lies in IV quadrant. When we rotate this point in 180° clockwise, then this point moves in II quadrant. So, new complex number will be R1​ R2​ Required complex number is Q1​ i.e., Q2​

Q. In the argand plane, the complex number $y = x$ is turned in the clockwise sense through 180? and stretched three times. The complex number represented by the new number is

$∴$

$(\frac{- 3 - y _{1}}{4 - x _{1}}) (1) = - 1$

$\Rightarrow$

$y_{1} + x_{1} = 1$

Given, $\frac{3}{2} M L^{2}$ $\frac{3}{4} M L^{2}$ $M L^{2}$ This complex number lies in IV quadrant. When we rotate this point in 180° clockwise, then this point moves in II quadrant. So, new complex number will be $R_{1}$ $R_{2}$ Required complex number is $Q_{1}$ i.e., $Q_{2}$