Respuesta :
Answer:
(a) In polar form complex number will be [tex]5.3851\angle 68.1985^{\circ}[/tex] and in radian argument is 0.378π
(b) [tex]6.0827\angle -9.46^{\circ}[/tex]
angle will be 0.05255π
Step-by-step explanation:
We have given
(a) 2+5i
We have to represent in polar form
We know that magnitude is given by [tex]\sqrt{(real\ part)^2+(imaginary\ part)^2}=\sqrt{2^2+5^2}=\sqrt{29}[/tex]
Argument is given by [tex]tan^{-1}\frac{imaginary\ part}{real\ part}=tan^{-1}\frac{5}{2}=68.198[/tex]
So in polar form complex number will be [tex]5.3851\angle 68.1985^{\circ}[/tex]
In radian argument will be [tex]68.1985\times \frac{\pi }{180}=0.378\pi[/tex]
(b) We have given complex number [tex]-6+i[/tex]
We know that magnitude is given by [tex]\sqrt{(real\ part)^2+(imaginary\ part)^2}=\sqrt{(-6)^2+1^2}=\sqrt{37}[/tex]
Argument is given by [tex]tan^{-1}\frac{imaginary\ part}{real\ part}=tan^{-1}\frac{1}{-6}=-9.46[/tex]
So in polar form complex number will be [tex]6.0827\angle -9.46^{\circ}[/tex]
In radian argument will be [tex]-9.46\times \frac{\pi }{180}=-0.05255\pi[/tex]
