Question

How do you find the complex conjugate of $3 - 2i$?

Answer 1

Hint: First we will reduce the term by mentioning all the rules. Then we will factorize the terms if possible. Then apply all the rules and evaluate the complex conjugate of the given term. Also, mention some points about conjugate of the complex number.

Complete step-by-step solution:
We will start off by explaining the conjugate of a complex number. So, a complex conjugate, simply changes the sign of the imaginary part which is the part with $i$. This means that it either goes from positive to negative or from negative to positive. As a general, the complex conjugate of $a + bi$ will be $a - bi$.
Hence, the complex conjugate of $3 - 2i$ is $3 + 2i$.

Additional information: The complex conjugate of a complex number is the number with an equal real part and an imaginary part equal in magnitude, but opposite in sign. Given a complex number $z = a + bi$ where $a$ and $b$ are real numbers, the complex conjugate is denoted by $\overline z $. Real numbers are only fixed points of conjugation. A complex number is equal to its complex conjugate if its imaginary part is zero. Composition of conjugate with the modulus is equivalent to the modulus alone.

Note: While calculating the conjugate you can also try the substitution method. You can multiply the numerator and denominator by the conjugate of the expression containing the square root. Also remember that the conjugate of a two-term expression is just the same expression with subtraction switched to addition or vice versa.