Question

Express 1+i²²+i²²⁰-i¹⁰⁰⁰ in the form of x+iy​

Answer 1

Step-by-step explanation:

i=√-1

i²= -1

(i²)^n=(-1)^n

(-1)^n is 1 if n is even

(-1)^n is -1 if n is odd

i²²=(i²)¹¹=(-1)¹¹= -1

i²²⁰=(i²)¹¹⁰=(-1)¹¹⁰=1

i¹⁰⁰⁰=(i²)⁵⁰⁰=(-1)⁵⁰⁰=1

1+i²²+i²²⁰-i¹⁰⁰⁰

1-1+1-1

0

x+iy=0+0i

x=0 and y=0

If you get 1+i²³+i³²

1+i²²(i)+i³²

1+(i²)¹¹(i)+(i²)¹⁶

1+(-1)¹¹(i)+(-1)¹⁶

1+(-1)i+1

1-i+1

2-i

Here x=2 and y= -1

hope it helps

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