Question

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

5/13
1(2/3)
2(3/5)
3

Answer 1

i have the answer

Explanation:

the correct answer is 2 and three fifths. good luck

Answer 2

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



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