If {(sqrt 8 + i)^{50}} = {3^{49}}(a + ib) the | vedclass

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

Question

(c) ${(\sqrt 8 + i)^{50}} = {3^{49}}(a + ib)$
Taking modulus and squaring on both sides, we get
${(8 + 1)^{50}} = {3^{98}}({a^2} + {b^2})$
${9^{50}

Vedclass · Accepted Answer

$9$

Vedclass · Answer

(c) ${(\sqrt 8 + i)^{50}} = {3^{49}}(a + ib)$
Taking modulus and squaring on both sides, we get
${(8 + 1)^{50}} = {3^{98}}({a^2} + {b^2})$
${9^{50}} = {3^{98}}({a^2} + {b^2})$
${3^{100}} = {3^{98}}({a^2} + {b^2})$
==> $({a^2} + {b^2}) = 9$.

If ${(\sqrt 8 + i)^{50}} = {3^{49}}(a + ib)$ then ${a^2} + {b^2}$ is

Similar Questions

Let $w$ $(Im\, w \neq 0)$ be a complex number. Then the set of all complex number $z$ satisfying the equation $w - \overline {w}z = k\left( {1 - z} \right)$ , for some real number $k$, is

Let $z$ be a complex number, then the equation ${z^4} + z + 2 = 0$ cannot have a root, such that

The value of $|z - 5|$if $z = x + iy$, is

Find the number of non-zero integral solutions of the equation $|1-i|^{x}=2^{x}$

If ${z_1}$ and ${z_2}$ are any two complex numbers then $|{z_1} + {z_2}{|^2}$ $ + |{z_1} - {z_2}{|^2}$ is equal to