Find the magnitude of (2-i)(1+3i)(3+4i)
First of all let's expand this
(2-i)(1+3i)(3+4i)
= (2-i)(3 + 13i + 12i^2)
= (2-i)(13i - 9) , remember that i^2 = -1
= 26i - 18 - 13i^2 + 9i
= -5 + 35i
magnitude
= √(25 + 1225)
= √1250
= 25√2
(2-i)(1+3i)(3+4i)
= (2-i)(3 + 13i + 12i^2)
= (2-i)(13i - 9) , remember that i^2 = -1
= 26i - 18 - 13i^2 + 9i
= -5 + 35i
magnitude
= √(25 + 1225)
= √1250
= 25√2