Question

Hello friends....☺☺

Answer 5,6,7,9 questions.

Answer 1

Hey mate here is ur query..
__________

i²=-1
i³=-i
i⁴=1
i^5=i
__________
hence
5......3i^5+2i⁴+5i³+4i²+1
=3i+2+(-5i)+(-4)+1
=3i-5i-1
=-2i-1 ==x+iy

i.e x=-2 and y =-1
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6...a.i^(135)= i^(4*33+3)=( i⁴)³³ * i³. =1³³ *-i =-i

..b..i^19= i⁴*⁴ * i³ = -i

..c..i^(-999)= i^(-250*4+1) =(i⁴)^(-250) *i¹
=1^(-250) * i= i

..d..[-(√-1)]^(4n+3) =[-i]^(4n+3)
=[(-i)⁴]^n * (-i)³
=1^n *(-1)³*i³
=1*(-1)*-i = i
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7... i^19=(i⁴*⁴) * i³ =-i.......... a
&
( 1/i)^25= i^(-25) =i^(-7*4+3)
=(i⁴)^(-7) * i³
=1^(-9) * (-i) =-i....... b

Given question=[i^19+(1/i)^25]²
Now puttng value from a & b
= [-i - i]²


=[-2i]² =-4 proved...
________________

9. put n =any natural no. find the result
let n=1 or any value u will find result 0

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Hope this will help you...

Answer 2

✔✔heya here is ur answer!!!

THANK YOU✌✌

HOPE IT HELPS YOU ☺☺