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Popular >

simplify ln(re^{iθ})

Solution

simplify

ln (r \cdot e^{i \cdot θ})

Solution

ln (r) + i θ

Solution steps

ln (r e^{i θ})

Apply log rule:

lo g_{c} (ab) = lo g_{c} (a) + lo g_{c} (b)

ln (r e^{i θ}) = ln (r) + ln (e^{i θ})

= ln (r) + ln (e^{i θ})

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

ln (e^{i θ}) = i θ ln (e)

= ln (r) + i θ ln (e)

i θ ln (e) = i θ

= ln (r) + i θ

Popular Examples

simplify-log_{10}(2.9*10^{-4})simplify

- lo g_{10} (2.9 \cdot 1 0^{- 4})

simplify-log_{10}(3.81*10^{-8})simplify

- lo g_{10} (3.81 \cdot 1 0^{- 8})

simplify log_{e}(((1-sin(y)))/(cos(2y)))simplify

lo g_{e} (\frac{( 1 - sin ( y ) )}{cos ( 2 y )})

simplify 1/3 (ln(4)-ln(3))simplify

\frac{1}{3} (ln (4) - ln (3))

simplify log_{10}(2*s(1-y)[y(2-y)]^{(s-1)})simplify

lo g_{10} (2 \cdot s (1 - y) [y (2 - y)]^{(s - 1)})

Frequently Asked Questions (FAQ)

What is ln(r*e^{i*θ}) ?
The solution to ln(r*e^{i*θ}) is ln(r)+iθ