Let {left( { - 2 - frac{1}{3}i} right)^3} = f | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) Given: ${\left( -2 - \frac{i}{3} ight)^3} = \frac{x + iy}{27}$Take out the negative sign: $-1 	imes {\left( 2 + \frac{i}{3} ight)^3} = \frac{

Vedclass · Accepted Answer

$91$

Vedclass · Answer

(A) Given: ${\left( -2 - \frac{i}{3} ight)^3} = \frac{x + iy}{27}$Take out the negative sign: $-1 	imes {\left( 2 + \frac{i}{3} ight)^3} = \frac{x + iy}{27}$Expand using $(a + b)^3 = a^3 + b^3 + 3a^2b + 3ab^2$:$-1 	imes \left[ 2^3 + \left( \frac{i}{3} ight)^3 + 3(2^2)\left( \frac{i}{3} ight) + 3(2)\left( \frac{i}{3} ight)^2 ight] = \frac{x + iy}{27}$$-1 	imes \left[ 8 - \frac{i}{27} + 4i - \frac{2}{3} ight] = \frac{x + iy}{27}$$-8 + \frac{2}{3} - i\left( 4 - \frac{1}{27} ight) = \frac{x + iy}{27}$Multiply by $27$:$x + iy = 27 	imes \left( -\frac{22}{3} ight) - i 	imes 27 	imes \left( \frac{107}{27} ight)$$x = -198$ and $y = -107$Then $y - x = -107 - (-198) = -107 + 198 = 91$

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

Similar Questions

If $(2x - y + 1) + i(x - 2y - 1) = 2 - 3i$,then the multiplicative inverse of $(x - iy)$ is

The real values of $x$ and $y$ for which the equation $({x^4} + 2xi) - (3{x^2} + yi) = (3 - 5i) + (1 + 2yi)$ is satisfied,are

If one root of the quadratic equation $ix^2 - 2(i + 1)x + (2 - i) = 0$ is $2 - i$,then the other root is

If ${\left( {\frac{{1 + i}}{{1 - i}}} \right)^m} = 1$,then the least integral value of $m$ is:

If ${\left( {\frac{{1 - i}}{{1 + i}}} \right)^{100}} = a + ib$,then

Vedclass Test Series

Exam Paper Generator

Online Exam Module