Respuesta :
Answer and explanation
(a) We have given that [tex]z_1=3+3\sqrt{3}i[/tex]
And [tex]z_2=1+\sqrt{3}i[/tex]
We have to prove that both complex number has same argument
Argument is given by [tex]\Theta =tan^{-1}(\frac{imaginary\ part}{real\ part})[/tex]
Argument of [tex]z_1=tan^{-1}\frac{3\sqrt{3}}{3}=tan^{-1}\sqrt{3}=60^{\circ}[/tex]
Argument of [tex]z_2=tan^{-1}\frac{\sqrt{3}}{1}=tan^{-1}\sqrt{3}=60^{\circ}[/tex]
Hence both [tex]z_!\ and\ z_2[/tex] have same argument
(b) We have given We have given that [tex]z_1=1+i[/tex]
And [tex]z_2=4+4i[/tex]
We have to prove that both complex number has same argument
Argument is given by [tex]\Theta =tan^{-1}(\frac{imaginary\ part}{real\ part})[/tex]
Argument of [tex]z_1=tan^{-1}\frac{1}{1}=tan^{-1}1=45^{\circ}[/tex]
Argument of [tex]z_2=tan^{-1}\frac{4}{4}=tan^{-1}1=45^{\circ}[/tex]
Hence both [tex]z_!\ and\ z_2[/tex] have same argument
