The result of adding a complex number to its conjugate is “an integer/a pure imaginary number/a real number/a whole number” and the result of subtracting a complex number from its conjugate is “an integer/a real number/a pure imaginary number/a whole number”

If Z is a complex number:

Z = a + b*i

where a and b are real numbers, and i is an imaginary number.

Then "a" is the real part.

"b*i" is the imaginary part.

The conjugate of Z is:

Zc = a - b*i

So the sign of the imaginary part changes.

Then:

Sum:

Z + Zc = (a + bi) + (a - bi) = 2*a + 0 = 2*a

and remember that a is a real number, then 2*a is also a real numer.

The correct answer is "A real number".

Difference:

Z - Zc = (a + bi) - (a - bi) = 2b*i

and this is a pure imaginary number, so here the correct answer is: "a pure imaginary number"

then, the surface area of the sphere shown in the image is: 256π sq. units!

step-by-step explanation:

the lateral surface area of a sphere is 2πrh where h=2r.

then:

surface area = 4πr^2.

in this case, r=8 units ⇒ surface area = 4π(8 units)^2. = 256π sq. units!

then, the surface area of the sphere shown in the image is: 256π sq. units!