complexnumberinpolarform我想问10∠5.91和10∠2.77是不是一样的?因为θ的范围是-π

Question

complex number in polar form
我想问10∠5.91 和10∠2.77 是不是一样的?
因为θ的范围是-π

Answer 1

If you want to know whether the two numbers are equal,you may expand them by Euler's formula 10∠5.91=10cos(5.91)+j10sin(5.91) 10∠2.77=10cos(2.77)+ j10sin(2.77).Therefore,it is apparent that the two numbers are not equal.
Now if the angle is in radians,we first notice π = 3.14 radian,and π / 2 = 1.57 radian.Further,for any angle x,sin(x - 2π) = sin(x),cos(x - 2π ) = cos(x),so 10∠5.91 = 10 ∠(5.91 - 2π) = 10 ∠ -1.09,which indeed falls in -π and π