JEE Maths›Complex Numbers & Quadratic Equations›Visual Solution
Visual SolutionPYQ 2024Easy
Question
If z=3+4iz = 3 + 4i, find ∣z∣|z|.
(A)55
(B)77
(C)7\sqrt{7}
(D)2525
Solution Path
∣z∣=32+42=25=5|z| = \sqrt{3^2 + 4^2} = \sqrt{25} = 5.
01Question Setup
1/4
Find ∣z∣|z| for z=3+4iz = 3 + 4i.
∣z∣=  ?|z| = \;?
02Modulus Formula
2/4
For z=a+biz = a + bi: ∣z∣=a2+b2|z| = \sqrt{a^2 + b^2}. Here a=3,b=4a = 3, b = 4.
∣z∣=32+42|z| = \sqrt{3^2 + 4^2}
03ComputeKEY INSIGHT
3/4
∣z∣=9+16=25=5|z| = \sqrt{9 + 16} = \sqrt{25} = 5.
25=5\sqrt{25} = 5
04Final Answer
4/4
∣z∣=5|z| = 5.
5\boxed{5}
Concepts from this question1 concepts unlocked
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Modulus Squared via Components

EASY

|a + bi|^2 = a^2 + b^2 - no square root needed

∣z∣2=z⋅zˉ=x2+y2|z|^2 = z \cdot \bar{z} = x^2 + y^2

Final step in many JEE problems. Students waste time square-rooting when they only need |z|^2

Distance problemsSum/product modulus\alpha^2 + \beta^2 type problems
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