What is i^4+i^3-3i^{16}+4i^5 ?

The solution to i^4+i^3-3i^{16}+4i^5 is -2+3i

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simplify i^4+i^3-3i^{16}+4i^5

simplify

i^{4} + i^{3} - 3 i^{16} + 4 i^{5}

- 2 + 3 i

Solution steps

i^{4} + i^{3} - 3 i^{16} + 4 i^{5}

i^{4} = 1

i^{3} = - i

3 i^{16} = 3

i^{5} = i

= 1 - i - 3 + 4 i

Group like terms

= - i + 4 i + 1 - 3

Add similar elements:

- i + 4 i = 3 i

= 3 i + 1 - 3

Subtract the numbers:

1 - 3 = - 2

= 3 i - 2

Rewrite in standard complex form:

- 2 + 3 i

= - 2 + 3 i

4 n - 4 m + 3 n - 5 m

512 + 8 m^{6}

ln (ln (e^{e^{8}}))

3 v - 5 v + 5 v + 4 v