Find $|9i-12|\cdot |3+4i|$.
To find the absolute value of a complex number, I need to use the formula $|a+bi|=\sqrt{a^2+b^2}$. So, for $|9i-12|$, I have $a=-12$ and $b=9$, and for $|3+4i|$, I have $a=3$ and $b=4$. Therefore, $|9i-12|=\sqrt{(-12)^2+9^2}=\sqrt{225}=15$ and $|3+4i|=\sqrt{3^2+4^2}=\sqrt{25}=5$. Now I just need to multiply these two absolute values. I get $|9i-12|\cdot |3+4i|=15\cdot 5=75$. 