Question

Find the complex conjugate of $3i - 4$. Choose the correct answer.
(A) $3i + 4$
(B) $- 3i - 4$
(C) $- 3i + 4$
(D) None of these

Answer 1

For finding the complex conjugate of any complex number we have to change the sign of the imaginary part of the complex number. So, by changing the sign of the complex number we get our answer.

Complete step-by-step answer:
A complex number is a number that can be expressed in the form $a + ib$, where a and b are real numbers, and i represents the imaginary unit.
As it is given in the question we have to find the complex conjugate of $3i - 4$.
Now we can write it as
$\Rightarrow 3i - 4 = - 4 + 3i$
Now for complex conjugate we change the sign of the imaginary part of the number i.e.
$\therefore + 3i \to - 3i$
But the sign of the real part remains the same i.e. $- 4$.
Now the complex conjugate of the given number we get by changing the sign is
$\Rightarrow 3i - 4 = - 4 - 3i$

So, the correct answer is “Option B”.

Additional Information:

1. Complex conjugate: The complex number which has an equal real part but an imaginary part equal in magnitude, and opposite in sign is the complex conjugate of a complex number.
2. Complex conjugate is represented by $\overline z$. The value of $\overline z$ is $\overline z = a - ib$, if $z = a + ib$.
3. The product of a complex number and its conjugate is always a real number.
4. If the imaginary part of the complex number is zero then it is equal to its complex conjugate.
5. With the help of complex conjugate we can find the roots of a polynomial.

Note: A complex number has both real and imaginary part. So we can find the complex conjugate of a complex number simply by changing the sign of the imaginary part of the complex number. The real part of the complex does not change. For this first write the complex number in the form of $a + ib$ and then change the sign of the imaginary part i.e $a - ib$.