Finite Math Examples

$\sin (2 a) + i \cos (2 a) = e^{z}$

Step 1

Rewrite the equation as $e^{z} = \sin (2 a) + i \cos (2 a)$ .

$e^{z} = \sin (2 a) + i \cos (2 a)$

Step 2

Take the natural logarithm of both sides of the equation to remove the variable from the exponent.

$\ln (e^{z}) = \ln (\sin (2 a) + i \cos (2 a))$

Step 3

Expand the left side.

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Step 3.1

Expand $\ln (e^{z})$ by moving $z$ outside the logarithm.

$z \ln (e) = \ln (\sin (2 a) + i \cos (2 a))$

Step 3.2

The natural logarithm of $e$ is $1$ .

$z \cdot 1 = \ln (\sin (2 a) + i \cos (2 a))$

Step 3.3

Multiply $z$ by $1$ .

$z = \ln (\sin (2 a) + i \cos (2 a))$