Question

Express √8 + 4 in the polar form and hence find its modulus and amplitude.​

Answer 1

Let z=

3

+i. Then, ∣z∣=

(

3

)

2

+(1)

2

=2.

Let θ be the argument of z and α be the acute angle given by tanα=

∣Re(z)∣

∣Im(z)∣

.

Then,

tanα=

3

1

⇒α=

6

π

Clearly, z lies in the first quadrant. So, arg(z)=α=

6

π

.