Number Theory T...

The principle amplitude of $$(\sin 40^{o}+i \cos 40^{o})^{5}$$ is

The value of the sum $$\sum _{ n=1 }^{ 13 }{ ({ i }^{ n }+{ i }^{ n+1 }) } $$ , where $$i=\sqrt { -1 } $$ , equals

$$z_1$$ and $$z_2$$ are two non-zero complex numbers such that $$z_1=2+4i\\z_2=5-6i$$, then $$z_2-z_1$$ equals

The imaginary part of $$t ; t \in R$$ is 

IF $$z_1=1+i,z_2=1-i$$ find $$z_1z_2$$

The real value of $$'\theta '$$, for which the expression $$\frac { 1+i\cos { \theta  }  }{ 1-2i\cos { \theta  }  } $$ is a real number is

The greatest and least value of $$\left | z \right |$$ if $$z$$ satisfies $$\left | z - 5 + 5i \right |$$ $$\leq 5$$ are 

let $$z=\left| \begin{matrix} 1 & 1+2i & -5i \\ 1-2i & -3 & 5+3i \\ 5i & 5-3i & 7 \end{matrix} \right|$$ then

How many prime numbers are there in the following series.
$$1,2,7,9,13,15,21,23,27,29$$

The imaginary roots of the equation $${ ({ x }^{ 2 }+2) }^{ 2 }+8{ x }^{ 2 }=6x({ x }^{ 2 }+2)$$ are ____________.