Complex Logarithms and Powers

Asked May 25 '21 at 16:09

Active May 25 '21 at 16:21

Viewed 47 times

Express each of the following complex numbers in Cartesian form (that is, in the form a+ib for a,b∈R), where Log denotes the Principal Complex Logarithm and the powers are Principal Complex Powers::

a) $$(ie)^{(i\pi)}$$

Note ($i\pi$) is the power for ($ie$) in this case sorry a bit new to this platform.

So I know this go down to like $$\exp(i\pi(\log(ie))$$

a bit confused on how to progress forward.

edited May 25 '21 at 16:21

Joe

2,671

asked May 25 '21 at 16:09

Max verstappen

1

Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to. – José Carlos Santos May 25 '21 at 16:13
Thankyou buddy I shall check it out :) – Max verstappen May 25 '21 at 16:14
Alright ok I shall try that out – Max verstappen May 25 '21 at 16:16
done thankyou hope this is slightly better now – Max verstappen May 25 '21 at 16:18
When you have an exponent with more than one character, you have to put it in braces. So, $e^\pi$ gives $e^\pi$, but for $e^{i\pi}$ we need $e^{i\pi}$ . – saulspatz May 25 '21 at 16:22
Thankyou I think someone helped me out with that. – Max verstappen May 25 '21 at 16:22
Would anyone mind solving this ? – Max verstappen May 25 '21 at 16:23
Have you looked at this https://math.stackexchange.com/questions/9770/understanding-imaginary-exponents and this https://math.stackexchange.com/questions/191572/prove-that-ii-is-a-real-number – Joe May 25 '21 at 16:34
yes i have but this is much more different than that – Max verstappen May 25 '21 at 16:36
What is the formula for $\log z$? – saulspatz May 25 '21 at 16:43
log(|z|)+iArg(z) – Max verstappen May 25 '21 at 16:45
Using that formula, what is $\log(ie)$? – Joe May 25 '21 at 16:47

Complex Logarithms and Powers

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