Question

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

Answer 1

a) i¹¹³ = i

b) i⁸² = -1

c) i⁴⁸ = 1

d) i²²³ = -1

Step-by-step 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!!!