
#1
Feb1014, 10:31 AM

P: 11

Hi,
We know that if we have two complex numbers in polar format (i.e., magnitude and exponential), that for two complex vectors z1 = A*exp(iB) z2 = C*exp(iD) If z1 and z2 are equal, then A = C and B = D. However, this is assuming these values are all real. What if they are complex? I.e. can we say if we have two complex numbers z3 = (a+ib)*exp(c+id) z4 = (e+if)*exp(g+ih) If z3 and z4 are equal, can we say that (a+ib) = (e+if) and (c+id) = (g+ih)? Thanks 



#2
Feb1014, 12:35 PM

P: 799





#3
Feb1014, 12:53 PM

P: 11





#4
Feb1014, 02:16 PM

Engineering
Sci Advisor
HW Helper
Thanks
P: 6,380

Equating Complex Numbersa = 1, b = c = d = 0, e = 0, f = 1, and find g and h to make z3 = z4. If you convert z3 = x3 + i y3 and z3 = x4 + i y4, you only have 2 equations (x3 = x4 and y3 = y4) but 8 unknowns (a through h). You need 6 more equations before you can hope there is a unique solution. 


Register to reply 
Related Discussions  
Equating differentials => equating coefficients  Classical Physics  9  
Strange real numbers requiring use of complex numbers to exist  General Math  7  
splitcomplex numbers and dual numbers  General Math  1  
Complex numbers representing Real numbers  General Math  3  
Complex numbers  are they the 'ultimate', or are there any "complex complex" numbers  Calculus  7 