Question

If z = (5 + 12i) ÷ (3 + 4i), then |z| = _____. 5/13 1(2/3) 2(3/5) 3

Answer 1

Answer:

i have the answer

Step-by-step explanation:

the correct answer is 2 and three fifths. good luck

Answer 2

$\dfrac{5+12i}{3+4i}=\dfrac{5+12i}{3+4i}\cdot\dfrac{3-4i}{3-4i}=\dfrac{15-20i+36i-49i^2}{3^2-(4i)^2}\\\\=\dfrac{15+16i+49}{9-16i^2}=\dfrac{64+16i}{9+16}=\dfrac{64+16i}{25}=2.56+0.64i$


$z=a+bi\\\\|z|=\sqrt{a^2+b^2}\\\\z=2.56+0.64i\to a=2.56;\ b=0.64\\\\|z|=\sqrt{2.56^2+0.64^2}=\sqrt{6.9632}=\sqrt{\dfrac{69632}{10000}}=\sqrt{\dfrac{4096\cdot17}{100}}\\\\=\dfrac{64\sqrt{17}}{100}=0.64\sqrt{17}\approx2.6=2\dfrac{3}{5}$