Respuesta :
a.
[tex] \sqrt{0+25} =5[/tex]
b.
[tex] \sqrt{ cos^{2} 5pi/7 +sin^{2} 5pi/7 } = \sqrt{1} =1[/tex]
I hope that this is the answer that you were looking for and it has helped you.
[tex] \sqrt{0+25} =5[/tex]
b.
[tex] \sqrt{ cos^{2} 5pi/7 +sin^{2} 5pi/7 } = \sqrt{1} =1[/tex]
I hope that this is the answer that you were looking for and it has helped you.
Answer and Explanation:
To find : Compute the modulus and argument of each complex number?
Solution :
a) [tex]-5i[/tex]
When the complex number is in the form [tex]z=a+ib[/tex]
Then the modulus of z is [tex]|z|=\sqrt{a^2+b^2}[/tex] and argument is [tex]\theta=\tan^{-1}(\frac{b}{a})[/tex]
On comparing with given complex number, a=0 and b=-5
Substitute in formulas,
The modulus of z is [tex]|z|=\sqrt{0^2+(-5)^2}=\sqrt{25}=5[/tex]
The argument of z is [tex]\theta=\tan^{-1}(\frac{-5}{0})=\tan^{-1}(\tan(90))=90^\circ[/tex]
b) [tex]\sqrt{10}(\cos(\frac{5\pi}{7})+i\sin(\frac{5\pi}{7}))[/tex]
When the complex number is in the polar form [tex]z=r(\cos\theta+i\sin\theta)[/tex]
Then the modulus of z is r and argument is [tex]\theta[/tex].
On comparing with given complex number,
The modulus of z is [tex]r=\sqrt{10}[/tex]
The argument of z is [tex]\theta=\frac{5\pi}{7}[/tex]
