Number Theory T...

Mark the correct alternative of the following.
Which of the following are not twin-primes?

Mark the correct alternative of the following.
Which of the following numbers are twin primes?

The total number of even prime numbers is?

Mark the correct alternative of the following.
Which of the following is a prime number?

Mark the correct alternative of the following.
The smallest number which is neither prime nor composite is?

Express the following complex numbers in the standard form $$ a+ib$$ :
$$ \left ( \dfrac{1}{1-4i}-\dfrac{2}{1+i} \right )\left ( \dfrac{3-4i}{5+i} \right )$$

Express the following complex numbers in the standard form $$ a+ib$$ :
$$ \dfrac{\left ( 2+i \right )^{3}}{2+3i}$$

Find the modulus and argument of the following complex numbers and hence express each of them in the polar form:
$$1-i$$

Express the following complex numbers in the standard from $$ a+ib$$ :
$$ \dfrac{5+\sqrt{2}i}{1-\sqrt{2}i}$$

Express the following complex numbers in the standard form $$ a+ib$$ :
$$ \dfrac{3-4i}{\left ( 4-2i \right )\left ( 1+i \right )}$$