If z - x - iy - z 1-3- a - i b and x - a - y - b - a 2- b 2- then - is equal toA- 3B- 4C- 1D- 2

The correct option is B 4 z^1/3 = a ib ⇒ x + iy =(a + ib)^3 = a^3 + ( ib)^3 3aib(a ib) ⇒ x + iy = a^3 + ib^3 3a^2bi 3ab^2 ⇒ x = a^3 3ab^2, y = b^3 ...

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

Byju's Answer

Standard XI

Mathematics

Inequality

If z = x + iy...

Question

If z = x + iy, $z^{\frac{1}{3}}$ = a - ib and $\frac{x}{a}$ - $\frac{y}{b}$ = $λ$ $(a^{2} - b^{2})$ , then $λ$ is equal to

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

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

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

Open in App

Solution

The correct option is C
4

$z^{\frac{1}{3}}$ = a - ib

$\Rightarrow$ x + iy = $(a + i b)^{3} = a^{3} + (- i b)^{3} - 3 a i b (a - i b)$

$\Rightarrow$ x + iy = $a^{3} + i b^{3} - 3 a^{2} b i - 3 a b^{2}$

$\Rightarrow$ x = $a^{3} - 3 a b^{2}$ , y = $b^{3} - 3 a^{2} b$

$\Rightarrow$ $\frac{x}{a}$ = $a^{2} - 3 b^{2}$ , $\frac{y}{b}$ = $b^{2} - 3 a^{2}$

∴ $\frac{x}{a}$ - $\frac{y}{b}$ = $4 (a^{2} - b^{2})$

Suggest Corrections

Similar questions

Q. If

z = x + i y

and

z^{1 / 3} = a - i b

, then

\frac{x}{a} - \frac{y}{b} = k (a^{2} - b^{2})

, where

k

is equal to

Q. If

z = x + i y, z^{1 / 3} = a - i b

and

\frac{x}{a} - \frac{y}{b} = k (a^{2} - b^{2}),

then

k =

Q. If

z = x + i y, z^{1 / 3} = a - i b

and

\frac{x}{a} - \frac{y}{b} = k (a^{2} - b^{2}),

then

k =

Q. If

\sqrt[3]{x + i y} = a + i b

then prove that

\frac{x}{a} + \frac{y}{b} = 4 (a^{2} - b^{2})

Q. If

z = x + i y

is a complex number such that

{¯ ¯ ¯ z}^{\frac{1}{3}} = a + i b

, then the value of

\frac{1}{a^{2} + b^{2}} (\frac{x}{a} + \frac{y}{b}) =

Join BYJU'S Learning Program

If z = x + iy, z13 = a - ib and xa - yb = λ(a2−b2), then λ is equal to

The correct option is C 4 z13 = a - ib ⇒ x + iy =(a+ib)3=a3+(−ib)3−3aib(a−ib) ⇒ x + iy = a3+ib3−3a2bi−3ab2 ⇒ x = a3−3ab2, y = b3−3a2b ⇒ xa = a2−3b2, yb = b2−3a2 ∴ xa - yb = 4(a2−b2)

If z = x + iy, $z^{\frac{1}{3}}$ = a - ib and $\frac{x}{a}$ - $\frac{y}{b}$ = $λ$ $(a^{2} - b^{2})$ , then $λ$ is equal to