What are the additive inverse of a complex number, conjugate of a complex number, Z + Z-bar, and degree of a rational function?

یہاں آپ کے سوالات کے جوابات ہیں۔

1. The additive inverse of $a+bi$ is $-a-bi$.

a) $\boxed{-a-bi}$

2. First, simplify the complex number:

$$(2+3i) + (1-i) = (2+1) + (3-1)i = 3+2i$$

The conjugate of $3+2i$ is $3-2i$.

c) $\boxed{3-2i}$

3. Given $Z = a+bi$.
The conjugate $\bar{Z} = a-bi$.
Then $Z+\bar{Z} = (a+bi) + (a-bi) = 2a$.

a) $\boxed{2a}$

4. The degree of the numerator $P(x) = 2x+5$ is 1.
The degree of the denominator $Q(x) = x^2-x+6$ is 2.
Since the degree of the numerator (1) is less than the degree of the denominator (2), the fraction is proper.

a) $\boxed{\text{Proper}}$

5. To find the partial fractions of $\frac{2x+3}{(x-