Question

What is the conjugate of the complex number $- 5 - 5i$?

Answer 1

Hint : Here, in the given question, we need to find the conjugate of the complex number $- 5 - 5i$. A complex number is just the addition of two parts, one real and one imaginary and it is written in the form of $a + ib$, where $a$ and $b$ are real numbers and $i$ is iota. For the complex number $z = a + ib$, $a$ is called the real part and $b$ is called the imaginary part. The complex number is denoted by $z$.

Complete step-by-step answer :
The conjugate of a complex number is also a complex number with the magnitudes of the real part and imaginary part as equal but the sign of the imaginary part is opposite. For example: the conjugate of $a + ib$ is $a + ib$. The conjugate of a complex number is denoted by $\overline z$.
Given, $- 5 - 5i$
Let complex number be $z = - 5 - 5i$.
As we know, the conjugate of a complex number is also a complex number with the magnitudes of the real part and imaginary part as equal but the sign of the imaginary part is opposite. Therefore, we get
$\Rightarrow \overline z = - 5 + 5i$
Hence, the conjugate of complex numbers $- 5 - 5i$ is $- 5 + 5i$.
So, the correct answer is “$- 5 + 5i$”.

Note : Remember that every real number is a complex number with the imaginary part as but not all complex numbers are real numbers. Also, remember that the conjugate of a complex number is the mirror reflection of the complex number along the x-axis. While converting a complex number to its conjugate, change the sign only of the imaginary part and not the real part of a complex number.