If 349(x+i y)=((3/2)+(√3 i/2))100 and x=k y, then k is

Question

If 349(x+i y)=((3/2)+(√3 i/2))100 and x=k y, then k is (A) √3 (B) (-1/√3) (C) (-1/3) (D) 3

Tardigrade Admin · Accepted Answer

349(x+i y)=((3/2)+(√3 i/2))100 =[i √3((1-i √3/2))]100 ⇒ 349(x+i y)=i100 ⋅ 350 ⋅(-ω)100 ⇒ 349(x+i y)=350 ⋅ ω=350((-1/2)+(i √3/2)) ∴ x+i y=-(3/2)+(3 √3 i/2) ⇒ x=-(1/√3) y ∴ k=-(1/√3)

Q. If $3^{49} (x + i y) = (\frac{3}{2} + \frac{3 i}{2})^{100}$ and $x = k y$ , then $k$ is

$3$

$\frac{- 1}{3}$

$\frac{- 1}{3}$

3

$3$

Q. If 349(x+iy)=(23​+23​i​)100 and x=ky, then k is

3​

3​−1​

3−1​

3

3​

349(x+iy)=(23​+23​i​)100 =[i3​(21−i3​​)]100 ⇒349(x+iy)=i100⋅350⋅(−ω)100 ⇒349(x+iy)=350⋅ω=350(2−1​+2i3​​) ∴x+iy=−23​+233i​​⇒x=−3​1​y ∴k=−3​1​

Q. If $3^{49} (x + i y) = (\frac{3}{2} + \frac{3 i}{2})^{100}$ and $x = k y$ , then $k$ is

$3$

$\frac{- 1}{3}$

$\frac{- 1}{3}$

$3$