Question

Evaluate
$i30 + i40 + i50 + i60$
Explain me
​

Answer 1

$\large \green{ \rm \:Question}$

$\large \green{ \: \: {i}^{30} + {i}^{40} + {i}^{50} + {i}^{60} }$

$\large \green{ \rm \:Solution}$

$\blue{ \: \: {i}^{30} + {i}^{40} + {i}^{50} + {i}^{60} }$

$\blue{ = {i}^{(4 \times 7)} {i}^{2} + {i}^{4 \times 10} + {i}^{(4 \times 12)} {i}^{2} + {i}^{(4\times15)} }$

$\green{ \: \: {i}^{4 \times n} = 1 }$

$\green{ \: \: {i}^{2} = - 1 }$

$\blue{ = {i}^{2} + 1+ {i}^{2} + 1 }$

$\blue{ = - 1+ 1 - 1+ 1 }$

$\blue{ = 0 }$