What is the datatype of the following expression? Show the flow line. int a, float b, short s, long g x = a + b*s – g/b;
write accurately I have to type
Answers
given
( x - iy) ( 3 + 5i) is the conjugate of -6 -24i
☆to find
find the values of real number x and y
☆ formula
[ i² = -1 ]
☆solution
The conjugate of -6 + 24i.
given, ( x - iy) ( 3 + 5i) = -6 + 24i
\begin{gathered}\longmapsto\pmb \: x - iy = \dfrac{ - 6 + 24i}{3 + 5i} \\ \\ \\\longmapsto\pmb \: x - iy = \dfrac{( - 6 + 24i)(3 - 5i)}{(3 + 5i)(3 - 5i)} \\ \\ \\ \longmapsto\pmb \: x - iy = \frac{ - 18 + 30i + 72i - 120i^{2} }{ {(3)}^{2} - {(5i)}^{2} } \\ \\\\ \end{gathered}
⟼
x−iy=
3+5i
−6+24i
⟼
x−iy=
(3+5i)(3−5i)
(−6+24i)(3−5i)
⟼
x−iy=
(3)
2
−(5i)
2
−18+30i+72i−120i
2
\begin{gathered}\longmapsto\pmb \: x - iy = \dfrac{ - 18 + 102i + 120}{9 - 25i^{2} } \qquad \qquad \red{ \{ {i}^{2} = - 1 \} }\\ \end{gathered}
⟼
x−iy=
9−25i
2
−18+102i+120
{i
2
=−1}
\begin{gathered}\longmapsto\pmb \: x - iy = \dfrac{102 + 102i}{9 + 25} \\ \\ \\ \longmapsto\pmb \: x - iy = \frac{102 + 120i}{34} \\ \\ \\ \longmapsto\pmb \: x - iy = \frac{102}{34} + \frac{102i}{34} \\ \\ \\ \longmapsto\pmb \: x - iy = 3 + 3i\end{gathered}
⟼
x−iy=
9+25
102+102i
⟼
x−iy=
34
102+120i
⟼
x−iy=
34
102
+
34
102i
⟼
x−iy=3+3i
\qquad \qquad \bigg \{ \boxed{\therefore \: x = 3 \: and \: y = - 3} \bigg \}{
∴x=3andy=−3
}
hence the value of x and y is 3 and -3