Math  /  Algebra

QuestionFind each of the following in rectangular form (a) sin(1i)\sin (1-i) (c) ln(e(1+i))\ln \left(-e^{(1+i)}\right) (b) i3/4i^{3 / 4} (d) ln(i+3)\ln (i+\sqrt{3})

Studdy Solution
(a) (e+1e)sin(1)2i(e1e)cos(1)2\frac{(e + \frac{1}{e})\sin(1)}{2} - i\frac{(e - \frac{1}{e})\cos(1)}{2} (b) cos(3π8+3πk2)+isin(3π8+3πk2)\cos(\frac{3\pi}{8} + \frac{3\pi k}{2}) + i\sin(\frac{3\pi}{8} + \frac{3\pi k}{2}) for k=0,1,2,3k = 0, 1, 2, 3 (c) 1+i(1+π+2πk)1 + i(1+\pi + 2\pi k) for integer kk (d) ln(2)+i(π6+2πk)\ln(2) + i(\frac{\pi}{6} + 2\pi k) for integer kk

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