JAMIA 2024 — Mathematics PYQ
JAMIA | Mathematics | 2024If ∣z1∣=4,∣z2∣=3 then what is the value of ∣z1+z2+3+4i∣?
Choose the correct answer:
- A.
Less than 2
- B.
Less than 5
- C.
Less than 7
- D.
Less than 12
(Correct Answer)
Less than 12
Explanation
Step 1: Identify the components
We are given:
-
∣z1∣=4
-
∣z2∣=3
-
Let the constant complex number be z3=3+4i.
Step 2: Calculate the magnitude of the constant
First, we find the modulus (magnitude) of z3=3+4i:
∣z3∣=32+42
∣z3∣=9+16
∣z3∣=25=5
Step 3: Apply the Triangle Inequality
To find the maximum value of the sum of these complex numbers, we add their individual magnitudes:
∣z1+z2+(3+4i)∣≤∣z1∣+∣z2∣+∣3+4i∣
Substitute the known values:
∣z1+z2+3+4i∣≤4+3+5
∣z1+z2+3+4i∣≤12
Explanation
Step 1: Identify the components
We are given:
-
∣z1∣=4
-
∣z2∣=3
-
Let the constant complex number be z3=3+4i.
Step 2: Calculate the magnitude of the constant
First, we find the modulus (magnitude) of z3=3+4i:
∣z3∣=32+42
∣z3∣=9+16
∣z3∣=25=5
Step 3: Apply the Triangle Inequality
To find the maximum value of the sum of these complex numbers, we add their individual magnitudes:
∣z1+z2+(3+4i)∣≤∣z1∣+∣z2∣+∣3+4i∣
Substitute the known values:
∣z1+z2+3+4i∣≤4+3+5
∣z1+z2+3+4i∣≤12