Goniometric form

Determine the goniometric form of a complex number

$z=\sqrt{110}+4i$

.

Correct answer:

Mod z =  11.22
Arg z =  20.88 °

Step-by-step explanation:

$Modz=\mathrm{\mid }z\mathrm{\mid }=\sqrt{(Rez{)}^2+(Imz{)}^2}=\sqrt{110+16}=11.22$

$$\begin{gathered} \tan \phi ={\displaystyle \frac{Imz}{Rez}}={\displaystyle \frac{4}{\sqrt{110}}}=0.381 \\ \phi =atan2(4,\sqrt{110}) \\ Argz=\phi =20.88^{\circ }=20^{\circ }52^{\mathrm{\prime }}34\mathrm{"} \\ z=\sqrt{110}+4i=11.22(\cos 20^{\circ }52^{\mathrm{\prime }}34\mathrm{"}+i\sin 20^{\circ }52^{\mathrm{\prime }}34\mathrm{"}) \end{gathered}$$

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