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Popular >

simplify ln(re^{iθ})

Solution

simplify

ln (r e^{i 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

expand ln((\sqrt[3]{x})/(10sqrt(yz)))expand

simplify log_{2}(x+1)+3log_{2}(x)-8log_{4}(x)simplify

lo g_{2} (x + 1) + 3 lo g_{2} (x) - 8 lo g_{4} (x)

simplify 1/2 log_{10}(c)+5log_{10}(d)simplify

\frac{1}{2} lo g_{10} (c) + 5 lo g_{10} (d)

expand log_{6}(x^4y^6)expand

lo g_{6} (x^{4} y^{6})

simplify 4ln(x)-1/8 ln(y)simplify

4 ln (x) - \frac{1}{8} ln (y)

Frequently Asked Questions (FAQ)

What is ln(re^{iθ}) ?
The solution to ln(re^{iθ}) is ln(r)+iθ