Question

please simplify i^37

Answer 1

do you know what i^2 = ?

Answer 2

no

Answer 3

the definition is \(\large i^2=-1 \)

Answer 4

notice that i^4 = (i^2)^2=(-1)^2

so i^4 = ???

Answer 5

\[i=\sqrt{-1}\]\[i ^{37}=i ^{36+1} = i \times i ^{36}=i \times (i ^{4})^{9}\]\[i ^{4}=\sqrt{-1}^{4}=(\sqrt{-1}^{2})^{2}=1^{2}=1\]
Thus,\[i \times (i^{4})^{9}=i \times (1)^{9}=i \times 1=i\]

Answer 6

so i?