Tag: complex numbers and linear inequations

$z _1$ and $z _2$ are two complex numbers such that $|z _1|= |z _2|$ and $arg (z _1)+arg(z _2)=\pi$, then $z _1$ is equal to

When simplified the value of $[i^{57}-(1/i^{25})]$ is?

The value of $i^{n}+i^{n+1}+i^{n+3}, n \epsilon N$ is 

The value of ${ i }^{ \frac { 1 }{ 3 }  }$ is:

The value of $\displaystyle\sum _{ n=0 }^{ 100 }{ { i }^{ n! } } $ equals ( where $i=\sqrt { -1 } $  ):

If $a ^ { 2 } + b ^ { 2 } = 1$, then $\dfrac { 1 + b + i a } { 1 + b - i a } = ?$

If ${(1+i)}^{2n}+{(1-i)}^{2n}=-{2}^{n+1}$ where, $i=\sqrt{-1}$ for all those $n$, which are

If $z + \frac{1}{z} = 2\cos {6^0}$, then ${z^{1000}} + \frac{1}{{{z^{1000}}}} + 1$ is equal to 

The value of $( 1 + i ) ^ { 4 } + ( 1 - i ) ^ { 4 }$ is

For positive integers $n _1, n _2, $ the value of the expression $(1 + i)^{n _1} + (1 + i^3)^{n _1} + (1 + i^5)^{n _2} + (1 + i^7)^{n _2}$, where $i = \sqrt{-1}$ is a