Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Main 201911 JanuaryMorning Shift
Exam
JEE Main
Year
2019
Date
11 January
Shift
Morning Shift
Subject
Mathematics
Chapter
Complex Number

JEE Main 2019 · 11 January · Morning Shift · Mathematics · Complex Number

Let (-2-(1)/(3) i)^ 3 =(x+i y)/(27)(i= -1 ), where x and y are real...

Let (−2−13i)3=x+iy27(i=−1),\left(-2-\frac{1}{3} i\right)^{3}=\frac{x+i y}{27}(i=\sqrt{-1}), where xandyx and y are real numbers then y−x\mathrm{y}-\mathrm{x} equals

Options

  1. A91
  2. B-85
  3. C85
  4. D-91

Correct answer

A. 91

Step-by-step solution

−(6+i)3=x+iy-(6+i)^{3}=x+i y ⇒−[216+i3+18i(6+i)]=x+iy\Rightarrow \quad-\left[216+i^{3}+18 i(6+i)\right]=x+i y ⇒−[216−i+108i−18]=x+iy\Rightarrow \quad-[216-i+108 i-18]=x+i y ⇒−216+i−108i+18=x+iy\Rightarrow \quad-216+i-108 i+18=x+i y ⇒−198−107i=x+iy\Rightarrow-198-107 i=x+i y ⇒x=−198,y=−107\Rightarrow \quad x=-198, y=-107 ⇒y−x=−107+198=91\Rightarrow \quad y-x=-107+198=91
Practice Complex Number on Quantrex Academy →

More from Complex Number

The number of values of z ∈ ℂ , satisfying the equations |z-(4+8i)|= 10 and… JEE Main 2026Let S = \ z ∈ ℂ : z^2 + 6 \,iz - 3 = 0\ . Then ∑ _ z ∈ S z^8 is equal to : JEE Main 2026Let the set of all values of k ∈ ℝ such that the equation z( z + 2 + i) + k(2 + 3i) = 0… JEE Main 2026Let z_1, z_2 ∈ ℂ be the distinct solutions of the equation z^2 + 4z - (1 + 12i) = 0 .… JEE Main 2026Let S=\ z ∈ ℂ: z^2+4z+16=0\ . Then ∑_ z ∈ S |z+ 3 i|^2 is equal to: JEE Main 2026Let z be a complex number such that |z+2| = |z-2| and ((z+3)/(z-i)) = (π)/(4) . Then… JEE Main 2026Let the circles C_1 : |z| = r and C_2 : |z - 3 - 4i| = 5 , z ∈ ℂ , be such that C_2 lies… JEE Main 2026Let x and y be real numbers such that 50((2x)/(1+3i) - (y)/(1-2i)) = 31 + 17i , i = -1 .… JEE Main 2026Let A=\ z ∈ ℂ:|z-2| 4\ and B=\ z ∈ ℂ:|z-2|+|z+2|=5\ . Then the max \ |z_ 1 -z_ 2 |: z_ 1… JEE Main 2026Let z be a complex number such that |z-6|=5 and |z+2-6 i|=5 . Then the value of z^ 3 +3… JEE Main 2026Let z=(1+i)(1+2 i)(1+3 i) …(1+n i) , where i= -1 . If |z|^ 2 =44200 , then n is equal to… JEE Main 2026If z= 3 2 +(i)/(2), i= -1 , then (z^ 201 -i)^ 8 is equal to JEE Main 2026Let S=\ z: 3 |2 z-3(1+i)| 7\ be a set of complex numbers. Then _ z ∈ S |(z+(1)/(2)(5+3… JEE Main 2026Let S=\ z ∈ ℂ: 4 z^ 2 + z =0\ . Then ∑_ z ∈ S |z|^ 2 is equal to: JEE Main 2026Let α= -1+i 3 2 and β= -1-i 3 2 , i= -1 . If (7-7 α+9 β)^ 20 +(9+7 α-7 β)^ 20 +(-7+9 α+7… JEE Main 2026Let z be the complex number satisfying |z-5| ≤ 3 and having maximum positive principal… JEE Main 2026 Full Complex Number list Complex Number JEE Maths PYQsJEE Mathematics PYQs All JEE Main PYQs