Solve this equation with steps please

Question

(-4+i)^3

 can you please solve this equation and please include the steps

Answer 1

(-4+i)³ = (-4+i)²(-4+i)

 

First compute (-4+i)² using the FOIL method.  Remember that i² = -1:

 

(-4+i)² = (-4+i)(-4+i) = (-4)²-4i-4i+i² = 16-8i-1 = 15-8i

 

Now multiply (-4+i)² = 15-8i by (-4+i) to get (-4+i)³:

 

(-4+i)³ = (-4+i)(15-8i) = -60+32i+15i-8i² = -60 + 47i +8 = -52+47i