Complex Numbers...

Find the modulus and the principal value of the argument of the number $$1-i$$

If i = $$\sqrt {-1}, then  1 + i^2 + i^3 -i^6 + i^8 $$ is equal to -

Solve $$\displaystyle \left ( 1-i \right )x+\left ( 1+i \right )y= 1-3i,$$

If $$z = \displaystyle \frac{(3 + 4i)(5 - 7 i)}{(7 + 5i)(4 - 3i)}$$ then $$|z| = ?$$

($$i^{10}+1) (i^9 + 1)(i^8 +1).......(i+1)$$  equal to 

The simplest form of the expression $$\dfrac {10 - \sqrt {-12}}{1 - \sqrt {-27}} $$ is

If $$i^2$$ $$= -1$$, then find the odd one out of the following expressions.

When $$(3-2i)$$ is subtracted from $$(4 + 7i)$$, then the result is

If $$u = 3 - 5i$$ and $$v = -6 + i$$, then the value of $$(u+v)^2$$ is