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[Music] so lets suppose we have a complex number z equals x plus i y and our problem is how to find the natural log of z all right so to begin with let me sketch my complex number on an argand diagram this is how my complex number looks like all right so i have the real axis i have the imaginary axis and this is my complex number z equals x plus i y suppose the modulus of this complex number is r so as you can see all right this uh all right lets also say the angle between the complex number and the real axis is theta we call that the argument of the complex number so this distance from here to here which is y is going to be r sine theta and this distance here is uh going to be x which is r cosine of theta so if i write this complex number again x plus i y i could also write it as r cos of theta plus i sine of theta so we call this the cartesian form of the complex number and we call this the polar form of the complex number so this is the polar form of writing the complex number no