Question

If |z1| = 4, |z2| = 3, then what is the value of |z1 + z2 + 3 + 4i|?

(a) Less than 2

(b) Less than 5

(c) Less than 7

(d) Less than 12

I had been asked this question at a job interview.

Question is from Quadratic Equations in portion Complex Numbers and Quadratic Equations of Mathematics – Class 11

Answer 1

Correct option is (d) Less than 12

For explanation: As, we know | z1 + z2 + …….. +zn| ≤ |z1| + |z2| + ………. + |zn|

So, |z1 + z2 + 3 + 4i| ≤ |z1| + |z2| + |3 + 4i|

Now, putting the given values in the equation, we get,

=> |z1 + z2 + 3 + 4i| ≤ 4 + 3 + √(9 + 16)

=> |z1 + z2 + 3 + 4i| ≤ 4 + 3 + 5

=> |z1 + z2 + 3 + 4i| ≤ 12.