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Exponentiation

During exponentiation with the imaginary unit as base, you get a development of

for the even powers           i ⁰ = 1,     i ² = –1,     i ⁴ = 1,     i ⁶ = –1,     etc.

for the odd powers            i ¹ =  i,     i ³ =  –i,     i ⁵ = i,      i ⁷ =  –i,     etc.

 

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Explanation

For the powers follows, clockwise

i ⁰ = 1 ,       i ¹ = i ,       i ² = –1 ,     i ³ = –i
i ⁴ = 1 ,       i ⁵ = i ,       i ⁶ = –1 ,     i ⁷ = –i

or counter-clockwise

i ⁰  = 1 ,     i ^–1 = –i ,     i ^–2 = –1 ,    i ^–3 =  i
i ^–4 = 1 ,     i ^–5 = –i ,     i ^–6 = –1 ,    i ^–7 =  i

This is often used for series developments.

 

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Argand diagram

In the complex plane can you draw a unit circle.

The Argand diagram shows the values 1, i, –1 and –i at the indicated points.

 

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