Find the modulus of each of the following:

Given: z = (1 + 2i)(i – 1)

Firstly, we calculate the (1 + 2i)(i – 1) and then find the modulus

So, we open the brackets,

$1(\mathrm{i}-1)+2 \mathrm{i}(\mathrm{i}-1)$

$=1(i)+(1)(-1)+2 i(i)+2 i(-1)$

$=i-1+2 i^{2}-2 i$

$=-i-1+2(-1)\left[\because i^{2}=-1\right]$

$=-i-1-2$

$=-i-3$

Now, we have to find the modulus of (-3 - i)

So, $|z|=|-3-i|=|-3+(-1) i|=\sqrt{(-3)^{2}+(-1)^{2}}=\sqrt{9+1}=\sqrt{10}$