Question

Question 2 Express the given complex number in the form a + ib: i^9 + i^19

Class X1 - Maths -Complex Numbers and Quadratic Equations Page 103

Answer 1

i^9 + i^(19)
= i^9 + i^(9 + 10)
we know,
a^(m+n) = a^m.a^n use this here,

= i^9 + i^9.i^10
=i^9(1 + i^10)
= i^9{ 1 + (i²)^5}
=i^9{ 1 + (-1)^5} [ use, i² = -1 ]
= i^9 { 1 - 1 }
= i^9 × 0
= 0 or 0 + 0i
hence, 0 + 0i , is the answer