According to our guidelines you are expected to show what you have attempted, or at least detail your thoughts on the problem.sw1 said:Express in the form a+ib:
(i+1)(i+2)(i+3)..(i+n)
I can handle problems like i^n, but this one has been giving me issues.
Complex numbers are numbers that contain both a real part and an imaginary part. They are written in the form a + bi, where a is the real part, b is the imaginary part, and i is the imaginary unit equal to the square root of -1.
To express a complex number in the form a+bi, you simply need to combine the real and imaginary parts. For example, if you have the complex number 3+4i, the real part is 3 and the imaginary part is 4, so the number can be expressed as 3+4i.
To add or subtract complex numbers, you simply add or subtract the real parts and the imaginary parts separately. For example, to add 3+4i and 2+5i, you would add 3+2 for the real parts and 4+5i for the imaginary parts, resulting in 5+9i.
To multiply complex numbers, you use the FOIL method, just like you would for multiplying binomials. First, you multiply the first terms, then the outer terms, then the inner terms, and finally the last terms. For example, to multiply (3+4i) and (2+5i), you would get 6+15i+8i+20i^2. Simplifying, you get 6+23i-20, or -14+23i.
To divide complex numbers, you use the conjugate of the denominator. The conjugate of a+bi is a-bi. You then multiply the numerator and denominator by the conjugate of the denominator. For example, to divide 4+7i by 2+3i, you would multiply both the numerator and denominator by 2-3i. This results in (8-12i+14i-21i^2)/(4-9i^2). Simplifying, you get (-13+2i)/13, or -1+i.