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Sagot :
Hello there. To solve this question, we have to remember some properties about conjugates and real (complex) numbers.
Suppose the expression
[tex]y+3[/tex]Is a real number, hence we know that
[tex]y[/tex]must also be a real number because the real numbers are a field and they are closed under addition.
The conjugate of a real number is then the real number itself, which means that
[tex]\overline{y+3}=y+3[/tex]Otherwise, if y is a complex number, it means it's imaginary part is not equal to zero.
Assuming y = a + bi for a, b real numbers and b not equal to zero, we have that
[tex]y+3=a+bi+3=(a+3)+bi[/tex]Hence the conjugate of this number is
[tex]\overline{(a+3)+bi}=(a+3)-bi[/tex]That is equivalent to have
[tex]\overline{y}+3[/tex]If y is a complex number.
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