evaluate the principal value of $i^{i+1}$ and derive a general expression for $\arccos(A)$, where $A$ is a real number $> 1$ and hence find $\arccos (3)$, writing your answer in the same form,
have to use quadratic equation that uses $\exp(iz)$
evaluate the principal value of $i^{i+1}$ and derive a general expression for $\arccos(A)$, where $A$ is a real number $> 1$ and hence find $\arccos (3)$, writing your answer in the same form,
have to use quadratic equation that uses $\exp(iz)$
$i^{i+1}=e^{ln(i)(i+1)}=e^{\pi/2*i(i+1)}=e^{-\pi/2+i \pi/2}=ie^{-\pi/2}$
Hint 1: $i=e^{i\pi/2}$
Hint 2: $A=\cos(x)=\dfrac{e^{ix}+e^{-ix}}2$