Question

find modulus and amplitude of
-3(1-i)​

Answer 1

$\huge\pink {Solution}$

Let z = -3+3i and let a be the acute angle given by tan a , that is :

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

Then we got :

tan a = |3|/|-3|

tan a = 1

we know that tan 45° = 1 , so a is 45° or we can write it as

tan a = tan π/4

a = π/4

We found that z is in 3rd quadrant ,so

arg.z = π- a

arg.z = π-π/4

arg.z = 3π/4

Also modulus of z is

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

|z| = √18