5e^(3+(i*pi)/6)=?

The given expression is 5e^(3+(i*pi)/6).

To simplify this, we can use Euler's formula, which states that e^(ix) = cos(x) + i*sin(x).

Step 1: Separate the real and imaginary parts of the exponent:

5e^(3) * e^((i*pi)/6)

Step 2: Apply Euler's formula to the second part:

5e^(3) * (cos(pi/6) + i*sin(pi/6))

Step 3: Calculate the values:

5e^(3) is approximately 100.458 cos(pi/6) is √3/2 sin(pi/6) is 1/2

Step 4: Substitute these values back into the equation:

100.458 * (√3/2 + i/2)

Step 5: Distribute 100.458:

50.229√3 + 50.229i

So, 5e^(3+(i*pi)/6) = 50.229√3 + 50.229i.