ln(exp(4*i)) — step-by-step solution

Let's calculate:

\ln (\exp (4 i))

ⓘ For the principal logarithm, keep the real part of the exponent and reduce its imaginary part to

(- π, π]

modulo

2 π

\ln (\exp (4 i))

i \times 4 - 2 i π

i \times 4 - 2 i π

ⓘ A complex number is written in algebraic form a + b*i, a being its real part and b its imaginary part:

i \times 4 - 2 i π

(4 - 2 π) \times i

(4 - 2 π) \times i

▶Result:

i \times (4 - 2 π)

The numeric value of:

i \times (4 - 2 π)

is:

i \times (4 - 2 \times \approx 3.1416)

i \times (4 - \approx 6.2832)

i \times \approx -2.2832

▷

- \approx 2.2832 i