Answered

Discover a wealth of knowledge at Westonci.ca, where experts provide answers to your most pressing questions. Join our platform to connect with experts ready to provide precise answers to your questions in different areas. Experience the ease of finding precise answers to your questions from a knowledgeable community of experts.

2.Drag the tiles to the correct boxes to complete the pairs.Match each complex number with its equivalent expression.-i1i-1119¡82i482234

2Drag The Tiles To The Correct Boxes To Complete The PairsMatch Each Complex Number With Its Equivalent Expressioni1i111982i482234 class=

Sagot :

Answer

a) i¹¹³ = i

b) i⁸² = -1

c) i⁴⁸ = 1

d) i²²³ = -1

Explanation

The complex number i, is expressed mathematically as

i = √(-1)

So,

i² = i × i = √(-1) × √(-1) = -1

i³ = i²× i = -1 × i = -i

i⁴ = i² × i² = -1 × -1 = 1

Hence, we can see that when the power on the complex number (i) is a multiple of 4, the answer will always be equal to 1.

So, this is the basis to solving all the expressions given.

a) i¹¹³

For 113, the closest multiple of 4 to this number is 112.

i¹¹³ = i¹¹² × i

i¹¹² = 1

i¹¹³ = i¹¹² × i = 1 × i = i

b) i⁸²

The closest multiple of 4 to the number 82, is 80.

i⁸² = i⁸⁰ × i²

i⁸⁰ = 1

i² = -1

i⁸² = i⁸⁰ × i² = 1 × -1 = -1

c) i⁴⁸

The number 48 is a multiple of 4, so,

i⁴⁸ = 1

d) i²²³

For the number 223, the closest multiple of 4 to this number is 220.

i²²³ = i²²⁰ × i³

i²²⁰ = 1

i³ = -i

i²²³ = i²²⁰ × i³ = 1 × -i = -i

Hope this Helps!!!

Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. Westonci.ca is your trusted source for answers. Visit us again to find more information on diverse topics.