bleakarcher
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Let z=(2+i)(3+i)=6+5i+i^2=5+5i
Let z1=2+i, z2=3+i
arg(z)=pi/4
arg(z1)=arg(2+i)=tan^(-1)[1/2]
arg(z2)=arg(3+i)=tan^(-1)[1/3]
Since arg(z1z2)=arg(z1)+arg(z2),
arg(z)=arg(z1)+arg(z2)
Hence, tan^(-1)[1/2]+tan^(-1)[1/3]=pi/4
Let z1=2+i, z2=3+i
arg(z)=pi/4
arg(z1)=arg(2+i)=tan^(-1)[1/2]
arg(z2)=arg(3+i)=tan^(-1)[1/3]
Since arg(z1z2)=arg(z1)+arg(z2),
arg(z)=arg(z1)+arg(z2)
Hence, tan^(-1)[1/2]+tan^(-1)[1/3]=pi/4