Express the given complex number in the form a + ib: i9 + i19
Question:

Express the given complex number in the form $a+i b: i^{9}+i^{19}$

Solution:

$i^{9}+i^{19}=i^{4 \times 2+1}+i^{4 \times 4+3}$

$=\left(i^{4}\right)^{2} \cdot i+\left(i^{4}\right)^{4} \cdot i^{3}$

$=1 \times i+1 \times(-i) \quad\left[i^{4}=1, i^{3}=-i\right]$

$=i+(-i)$

$=0$

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