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Q)

Express the complex number $i^{9}+i^{19}$ in the form $a+bi$

$(a)\;3\qquad(b)\;1\qquad(c)\;0\qquad(d)\;2$

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A)
Answer : 0
Explanation :
$i^{9} + i^{19} = i^{4\times 2 + 1 } + i^{4 \times 4 + 3}$
$= (i^4)^{2}\;.i +(i^{4})^{4} \;.i^{3}$
$= 1 \times \;.i + 1 \times \;.(-i) \qquad [i^{4} = 1\;, i^{3} = -i]$
$=i - i$
$=0$
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