Question

e^z=-3+4i,z是多少? 求解!

Answer 1

-3+4i=5e^iθ,tanθ=-4/3
e^z=e^(x+iy)=e^x*e^Iy
e^z=-3+4i
模与夹角分别对应相等
e^x=5,e^iθ=e^Iy
x=ln5,y=θ=-actan4/3
考虑多值函数
所以z=ln5-iactan(4/3+2kπ）k=0,±1,±2,±3.
望采纳