Calculate Ln(i^i)

evitagimm9h

evitagimm9h

Answered question

2022-11-12

Calculate Ln ( i i )
My attempt:
Ln ( z )= ln | z | + i arg z
z = 0 + i i = 0 + i i
| z | = 0 2 + i 2 = i arg z = arctan ( i / 0 )
1. how it can be that the modulus equal to i?
2. how can I find the argument?

Answer & Explanation

Falpo359

Falpo359

Beginner2022-11-13Added 15 answers

As i = cos π / 2 + i sin π / 2 = e i π / 2
i i = e i Ln ( i ) = e 2 n π i + i π / 2 i = e 2 n π i π / 2
Ln ( i i ) = 2 n π i π / 2 where n is any integer

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