- #1
Allday
- 164
- 1
How do you evaluate this expression algebraically.
[tex]
e^{\sqrt{i}}
[/tex]
[tex]
e^{\sqrt{i}}
[/tex]
Complex numbers are numbers that contain both a real and imaginary part. They are written in the form a + bi, where a is the real part and bi is the imaginary part, and i is the imaginary unit equal to the square root of -1.
To add or subtract complex numbers, simply combine the real parts and the imaginary parts separately. For example, (3+2i) + (5+4i) = (3+5) + (2i+4i) = 8 + 6i. To subtract, follow the same process but subtract the corresponding parts instead of adding them.
The conjugate of a complex number is found by changing the sign between the real and imaginary parts. For example, the conjugate of 4+3i is 4-3i. This is important in dividing complex numbers and simplifying expressions.
To multiply complex numbers, use the FOIL (First, Outer, Inner, Last) method. For example, (4+2i)(3+5i) = 12 + 20i + 6i + 10i^2 = 12 + 26i - 10 = 2 + 26i. To divide, multiply the numerator and denominator by the conjugate of the denominator, then simplify.
The absolute value (or modulus) of a complex number is its distance from the origin on the complex plane. It is found by taking the square root of the sum of the squares of the real and imaginary parts. For example, the absolute value of 4+3i is sqrt(4^2 + 3^2) = 5.