Question

question 18 of 45
let ( z = 4 + 5i ) and ( w = 3 + 7i ), where ( i ) is the imaginary unit. what is the value of ( 2z + w )?
a ( 10 + 19i )
b ( 11 + 12i )
c ( 11 + 17i )
d ( 14 + 24i )

Explanation:

Step1: Calculate \(2z\)

Given \(z = 4 + 5i\), multiply by 2: \(2z = 2(4 + 5i) = 8 + 10i\)

Step2: Add \(w\) to \(2z\)

Given \(w = 3 + 7i\), add to \(2z\): \((8 + 10i) + (3 + 7i) = (8 + 3) + (10i + 7i) = 11 + 17i\)

Answer:

C. \(11 + 17i\)