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A question on complex numbers?
If arg(z-1)=1/3pi and arg(z-i)=1/6pi, what is arg(z)?
Please include explanations in your workings! Thanks!
2 Answers
- ?Lv 79 years agoFavorite Answer
Draw complex plane graph, a circle and the two arg lines (π/6 and π/3). Plot line arg(z) falls on.
z=π/4
- Elizabeth MLv 79 years ago
If z=a+ib then arg(a-1+ib)=(1/3)pi so b/(a-1)=tan[(1/3)pi]=sqrt(3) so b=(a-1)sqrt(3).
arg(a+i(b-1))=(1/6)pi so a+i(b-1)=tan[(1/6)pi]so (b-1)/a = 1/sqrt(3) and b-1=a/sqrt(3)
Solve the two equations to find a and b. You should get a=b giving arg(z)=(1/4)pi.
You might be able see this from the symmetry of the figure.
