Question

How do you find the conjugate of $7-5i$ ?

Answer 1

Hint: From the question given we have to find the conjugate of $7-5i$. As we know that given number is complex number, complex number means the number that can be expressed in the form$a+bi$ where a and b are real numbers, and I is a symbol called the imaginary unit, and satisfying the equation ${{i}^{2}}=-1$. As we know that the complex conjugate of $a+bi$ is $a-bi$, that is you have to simply change the sign of the imaginary component. By this we can find the complex conjugate of the given complex number.

Complete step by step solution:
From the question given we have to find the complex conjugate of
$\Rightarrow 7-5i$
 As we know that given number is complex number, complex number means the number that can be expressed in the form
$\Rightarrow a+bi$
where a and b are real numbers, and I is a symbol called the imaginary unit, and satisfying the equation
$\Rightarrow {{i}^{2}}=-1$
As we know that the complex conjugate of $a+bi$ is
$\Rightarrow a-bi$
we have to simply change the sign of the imaginary component.
By this we can write that the complex conjugate of $7-5i$ is
Simply we have to change the sign of the imaginary component, that is
$\Rightarrow 7+5i$
Therefore, this required a complex conjugate of $7-5i$

Note: Students should recall the all the concepts of complex numbers while doing this problem, student should note that the complex conjugate of a complex number can be written by changing the sign of imaginary part not real part, for suppose the complex conjugate of $a+bi$ is $a-bi$ not $-a+bi$.