How to find a modulus and argument of w that is a quotient of z1 and z2 such that z1 = 1 + root(3)i and z2 = 1+ i using modulus-argument form?
First of all, transform both z1 and z2 into modulus-argument form. To obtain that form, you are going to need a modulus (the length of the hypotenuse on the Argand diagram) and argument (the angle between opposite and adjacent). Modulus can be simply calculated using the Pythagoras's equation, so: modulus of z1 is equal to the root of the sum of the squared lengths of both opposite and adjacent. In this case, modulus z1 = 2 and modulus z2 = root of 2. Getting angles is easy too. Simply calculate arctan of imaginary/real, but remember to draw the triangle on the diagram, as it is easy to make a mistake here, especially when dealing with angles in 3rd and 4th quadrants. The obtained angles should be pi/3 and pi/4.
Now onto the modulus-argument form. The general formula is: mod(z)[cos(arg) + isin(arg)], so try following that.
After doing so, to get mod(w) divide mod(z1) and mod(z2) as w is a quotient. The argument is arg(z1) - arg(z2).
