Question 2:

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

Answer

i⁹ + i¹⁹ = i^4×2+1 + i^4×4+3            

              =(i⁴)² ∙ i + (i⁴)⁴ ∙ i³              

              = 1 × i +1×(−i)              [i⁴ = 1, i³ = −i]              

              = i + (−i)

              = 0

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