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Let z be a complex number satisfying 2z+\(3\overline{z}\)=-25-2i

What is the value of z?

 Oct 3, 2022
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\(z = a + bi\) 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, \(z = -5 + 2i\).

 Oct 3, 2022

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