Number Theory T...

$$\left| \dfrac { (3+i)(2-i) }{ 1+i }  \right|=$$

If $$(a_1+ib_1)(a_2+ib_2)...(a_n+ib_n)=A+iB$$ then $$(a_1^2+b_1^2)(a_2^2+b_2^2)...(a_n^2+b_n^2)=$$

The simplified value of $$\displaystyle \frac{1-i}{1+i}$$ is:

If $$\left ( 5+3i \right )(x+iy)=3-4i$$ then $$34x = $$

The value of $$1+(1+i)+(1+i)^2+(1+i)^3=$$

If $$z=-1+3i$$ then $$z^2+2z+10=$$

If $$\alpha $$ and $$\beta $$ are real then $$\left| \dfrac { \alpha +i\beta  }{ \beta +i\alpha  }  \right|=$$ 

If $$(x+iy)(2-3i)=4+i\left ( \dfrac{1}{2} \right )$$ then $$x + y =$$

The minimum value of $$|\mathrm{z}|+|\mathrm{z}-1|+|\mathrm{z}-2|$$ is

If $$m_1$$, $$m_2$$, $$m_3$$ and $$m_4$$ respectively denote the moduli of the complex numbers $$1 + 4i, 3 + i, 1 – i \ and\  2 – 3i$$ then the correct order among the following is :