3i^12+2i^15-4i^17+i^26

Question

using imaginary numbers 

Answer 1

To find i to a positive integer power greater than 4, divide the power by 4 and replace the power by the remainder found in the division process.

 

Dividing 12 by 4 gives a remainder of 0

Dividing 15 by 4 gives a remainder of 3

Dividing 17 by 4 gives a remainder of 1

Dividing 26 by 4 gives a remainder of 2

 

3i¹² + 2i¹⁵ - 4i¹⁷ + i²⁶ = 3i⁰ + 2i³ - 4i¹ + i² = 3(1) + 2i³ - 4i + i²

 

                                                                         = 3 - 2i - 4i -1

 

                                                                         = 2 - 6i