Which simplifications of the powers of i are correct? There may be more than one correct answer. Select all correct answers. A) i^6=1 B) i^18=1 C) i^7=-i D) i^16=1
Accepted Solution
A:
Answer:Option C and D are correct optionsStep-by-step explanation:The correct options are C and D.We know that i = √-1i² = -1i³ = -iand i^4 = 1Lets solve the options one by one:i^6 =1Break the power:i² *i ² * i² = (-1)(-1)(-1)= -1 Therefore A is wrongB) i^18 = 1Lets break the power:i²* i² *i² *i²*i²*i²*i²*i²*i²put the value of i^2= (-1) (-1) (-1) (-1) (-1) (-1) (-1) (-1)(-1)= -1Therefore option B is incorrect.C) i^7 = -i= i² * i² *i² *i=(-1) (-1) (-1) * √-1= - √-1We know that √-1 = iSo, - √-1 = -iTherefore option C is correct.D) i^16 = 1= i² * i² * i² * i² * i² * i² *i² *i²= (-1) (-1) (-1) (-1) (-1) (-1) (-1) (-1)= 1Therefore option D is correct.Thus option C and D are correct option....