Answer:
Step-by-step explanation:
(a)[tex]\left ( 1+i\right )^2[/tex]
[tex]=1+i^2+2i=1-1+2i[/tex]
[tex]=0+2i[/tex]
(b)[tex]\left ( 1+i\right )^4[/tex]
using above i.e.
[tex]\left ( 1+i\right )^2=2i[/tex]
[tex]\left ( 2i\right )\left ( 2i\right )=4i^2[/tex]
[tex]=-4+i0[/tex]
(c)[tex]\left ( 1+i\right )^6[/tex]
Using above two results
[tex]=\left ( 1+i\right )^2\cdot \left ( 1+i\right )^4[/tex]
[tex]=\left ( 2i\right )\left ( -4\right )[/tex]
[tex]=-8i[/tex]
[tex]=0-8i[/tex]
