Given #z# is a complex number such that #Arg(z) = theta# and #|z| = r# , write an expression for each of #Arg(4z^3)# and #|4z^3|# in terms of r and/or θ. How should I approach this?

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Answer 1 · 2018-06-09T06:53:16

Contd.........

A complex no. #z# is such that #Arg(z)=theta and |z|=r#.

Clearly, #z=r(costheta+isintheta)#.

By De Moivre's Theorem, #z^n=r^n(cosntheta+isinntheta)#.

#:. z^3=r^3(cos3theta+isin3theta)#.

#:. 4z^3=4r^3(cos3theta+isin3theta)#.

Answer 2 · 2018-06-09T07:06:52

#z = r e^(i theta)#

#4 z^3 = 4(r e^(i theta))^3 = 4 r^3 e^(i 3 theta) #