Question

The complex number z=1+i^10+i^20+i^30 is
A) zero
B)an imaginary number
C) a complex number
D) a real number
with Explanation​

Answer 1

Answer:

The answer to this question is 0

Step-by-step explanation:

We know that, $\iota^2 = -1$

Now,

$1 + \iota^{10} + \iota^{20} + \iota^{30}\\= 1 + (\iota^{2})^5 + (\iota^{2})^{10} + (\iota^{2} )^{15}\\= 1 + (-1)^5 + (-1)^{10}+(-1)^{15}\\= 1 -1 +1 -1\\=0$