lily

12-27-2013, 04:42 AM

SAT subject mathematics Complex numbers

Which of the following is equal to i^{2013}?

(A) i

(B) -i

(C) 1

(D) -1

(E) 2i

Thanks!:D

Which of the following is equal to i^{2013}?

(A) i

(B) -i

(C) 1

(D) -1

(E) 2i

Thanks!:D

View Full Version : SAT subject mathematics Complex numbers

lily

12-27-2013, 04:42 AM

SAT subject mathematics Complex numbers

Which of the following is equal to i^{2013}?

(A) i

(B) -i

(C) 1

(D) -1

(E) 2i

Thanks!:D

Which of the following is equal to i^{2013}?

(A) i

(B) -i

(C) 1

(D) -1

(E) 2i

Thanks!:D

miranda

12-27-2013, 04:44 AM

We know that for the imaginary unit i hold the following

i^2=-1,

i^3= i^2 \cdot i=(-1) \cdot i=-i

and i^4=(i^2)^2=(-1)^2=1.

Also, 2013 can be written as 4*503+1

So, i^{2013}=(i^4)^{503} \cdot i^1=1 \cdot i=i

Therefore the correct answer is (A).

Hope these help!!:)

i^2=-1,

i^3= i^2 \cdot i=(-1) \cdot i=-i

and i^4=(i^2)^2=(-1)^2=1.

Also, 2013 can be written as 4*503+1

So, i^{2013}=(i^4)^{503} \cdot i^1=1 \cdot i=i

Therefore the correct answer is (A).

Hope these help!!:)

lily

12-27-2013, 04:45 AM

We know that for the imaginary unit i hold the following

i^2=-1,

i^3= i^2 \cdot i=(-1) \cdot i=-i

and i^4=(i^2)^2=(-1)^2=1.

Also, 2013 can be written as 4*503+1

So, i^{2013}=(i^4)^{503} \cdot i^1=1 \cdot i=i

Therefore the correct answer is (A).

Hope these help!!:)

Thank you:)

i^2=-1,

i^3= i^2 \cdot i=(-1) \cdot i=-i

and i^4=(i^2)^2=(-1)^2=1.

Also, 2013 can be written as 4*503+1

So, i^{2013}=(i^4)^{503} \cdot i^1=1 \cdot i=i

Therefore the correct answer is (A).

Hope these help!!:)

Thank you:)

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