z = 50 / (3+4i). What is z in a+bi form?

Multiply by complex conjugate

z = 50 / (3+4i) * (3-4i) / (3-4i)

Rationalise

z = 50 ( 3 - 4i) / 25 = 6 - 8i.

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Using a Taylor's series or otherwise; derive Euler's Formula


MEI (OCR) M4 June 2006 Q3


Prove by induction that the sum of the first n integers can be written as (1/2)(n)(n+1).


Let I(n) = integral from 1 to e of (ln(x)^n)/(x^2) dx where n is a natural number. Firstly find I(0). Show that I(n) = -(1/e) + n*I(n-1). Using this formula find I(1).


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