Complex Sum From Complex Nos

Algebra Level 2

$\large i \sqrt{i} = \ ?$

Notation: $i =\sqrt {-1}$ is the imaginary unit .

\frac{ -1 + i } { \sqrt{2}}

\frac{ i - \sqrt{3 } } {2}

\frac{ 1 + i } { \sqrt{2}}

\frac{ i + \sqrt{3} } { 2 }

2 solutions

Elaaf Salem
Aug 2, 2016

$-1 = e^{iπ}$

$i = e^{i*π/2}$

$\sqrt{i} = e^{i*π/4}$

now we have : $i \sqrt{i}$ = $e^{i*π/2}$ * $e^{i*π/4}$ = $e^{i*3π/4}$

$e^{ix} = cos(x) + i sin(x)$

$e^{i*3π/4} = -1 / \sqrt{2} + i * 1 / \sqrt{2}$

$= 1 / \sqrt{2} (-1+i)$

That is what i was saying

Md Zuhair - 4 years, 10 months ago

Md Zuhair
Jul 29, 2016

$irooti$ can be written as iroot (cos pi/2 + isin pi/2) ...... And by simplyfing taking the Euler Form ... we get the ans.