Number Theory T...

Dividing $$ f(z) $$ by $$ z - i$$ we obtain the remainder i and dividing it by $$ z + i$$ we get the remainder $$1 + i$$ then remainder upon the division of $$ f(z)$$ by $$ z^{2} + 1$$ is

Evaluate in standard form: $$\dfrac {(2-3i)}{(2-2i)}$$, where $${i}^{2}=-1$$.

Express in the form of a complex number $$a+bi$$
$$-(7-i)(-4-2i)(2-i)$$

The numbers which have more than two factors are called ______.

In binary system the highest value of a 8-bit number is

The $$3$$ bit operation code for ADD operation is $$001$$ and indirect memory address is $$23$$ then $$16$$-bit instruction code can be written as-

Let $$z_1$$ = 18 + 83i, $$z_2$$ = 18 + 39i, ana $$z_3 $$= 78 + 99i. where i = $$\sqrt-1$$. Let z be a unique comlpex number with the properties that $$\dfrac{z_3 - z_1}{z_2 - z_1}$$ $$\cdot$$ $$\dfrac{z - z_2}{z - z_3}$$ is a real number and the imaginary part of the size z is the greatest possible.

If $$z$$ is a complex number such that $$|z|\geq 2$$ then the minimum value of $$\left |z + \dfrac {1}{2}\right |$$ is

If $$z_ 1 = 2 \sqrt 2 (1 + i)$$ and $$z = 1 + i \sqrt 3$$, then $$z_1^2 z_2^3$$ is equal to

If $$z_1+ z_2 + z_3 = 0$$ and $$|z_1|=|z_2|=|z_3|= 1$$, then area of triangle whose vertices are $$z_1, z_2$$ and $$z_3$$ is: