Let z be a complex number satisfying 2z+\(3\overline{z}\)=-25-2i
What is the value of z?
+1622 \(z = a + bi\) where a and b are real numbers and i is one unit in the imaginary plane.
\(2(a + bi) + 3(a - bi) = -25 - 2i\)
\(2a + 2bi + 3a - 3bi = -25 - 2i\)
\(5a - bi = -25 - 2i\)
The real number parts of the equation are equal and the imaginary parts of the equation are equal:
\(5a = -25\)
\(-bi = -2i\)
Now, we can obtain that \(a = -5\) and \(b= 2\).
Thus, \(z = -5 + 2i\).
