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# complex numbers

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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

#1
+1015
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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