Question:
Find the modulus of each of the following:
$(1+2 i)(i-1)$
Solution:
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, $|z|=|-3-i|=|-3+(-1) i|=\sqrt{(-3)^{2}+(-1)^{2}}=\sqrt{9+1}=\sqrt{10}$
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