Vis at ∣z1z2∣=∣z1∣∣z2∣|z_1 z_2|=|z_1||z_2|∣z1z2∣=∣z1∣∣z2∣.
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Bruk definisjonen sinz=eiz−e−iz2i\displaystyle \sin z = \frac{e^{iz}-e^{-iz}}{2i}sinz=2ieiz−e−iz:
sin(i)=ei⋅i−e−i⋅i2i=e−1−e12i=−(e−e−1)2i\displaystyle \sin(i) = \frac{e^{i\cdot i}-e^{-i\cdot i}}{2i} = \frac{e^{-1}-e^1}{2i} = \frac{-(e-e^{-1})}{2i}sin(i)=2iei⋅i−e−i⋅i=2ie−1−e1=2i−(e−e−1)
Gang med ii\displaystyle \frac{i}{i}ii: =−i(e−e−1)2i2=i(e−e−1)2=isinh(1)≈1,175i\displaystyle = \frac{-i(e-e^{-1})}{2i^2} = \frac{i(e-e^{-1})}{2} = i\sinh(1) \approx 1{,}175i=2i2−i(e−e−1)=2i(e−e−1)=isinh(1)≈1,175i
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