# Pre-exam. algebra questions.

• fasterthanjoao

#### fasterthanjoao

1) Sketch the regions in the Argand diagram given by:

|z+i| < |z-3|

this means the distance from z to 3 is greater than the distance from z to i? would I then just draw two lines on the argand diagram, shading the lower region and not including the boundary? haven't had a problem with these questions through term, guess I am just a bit burned out and need to make sure. :uhh:

2) Find the modulus and the argument of:
1+ cosx + isinx

does this involve changing the angle to x/2 and using trig expansions?

-thanks.

fasterthanjoao said:
1) Sketch the regions in the Argand diagram given by:

|z+i| < |z-3|

this means the distance from z to 3 is greater than the distance from z to i? would I then just draw two lines on the argand diagram, shading the lower region and not including the boundary? haven't had a problem with these questions through term, guess I am just a bit burned out and need to make sure. :uhh:

2) Find the modulus and the argument of:
1+ cosx + isinx

does this involve changing the angle to x/2 and using trig expansions?

-thanks.

In this case it is useful to express these complex numbers as z = a+ib and then calculate the modulus. You know that a is on the x-axis and y is on the imaginary y-axis...