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Complex Numbers

Complex Algebra, Magnitude

jee_main_2026_april_4_shift_2

Grade 12

Question:

If z = 2 + 4i and w = 1 - 2i, and |z + w| = √k, then the value of k is:

A. 5

B. 13

C. 18

D. 20

Step-by-Step Solution

Key Concept: First compute z + w, then find its magnitude.

Step 1: z + w = (2+1) + (4-2)i = 3 + 2i. Step 2: |z + w| = √(3^2 + 2^2) = √13. Step 3: Hence k = 13.

Correct Answer: B

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