Question

If z=1+3i,find the modulus and amplitude of z.​

Answer 1

Answer -

ARG(z) = π/3 and modulus of z is 2

Solution-

As z = 1 +√3i , let a be the acute angle given by

$\tan(a) = | \frac{im(z)}{re(z)} |$

$\tan(a) = | \frac{ \sqrt{} 3}{1} |$

tan a = √3

tan a = tan π/3

a. = π/3

We observe that z lies in 1st quadrant , So.

ARG(z) = a = π/3

$|z| = \sqrt{( {1)}^{2} + ( { \sqrt{3}) }^{2} }$

| z | = 2

Answer 2

Given : z=1+3i

To Find :  Modulus

Solution:

 z=1+3i

Modulus  z = | z |  

= √1² + 3²

= √1 + 9

= √10

Modulus  of =1+3i  =  √10

amplitude of z = arg z =  Tan⁻¹( 3/1)

=>amplitude of z =   Tan⁻¹( 3)

=> amplitude of z =  71.565°  or 1.249 rad

amplitude of 1+3i  =  1.249   ( as its measured in radian )

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