Complex NumbersHard

Question

Let z1and z2 be nth roots of unity which subtend a right angled at the origin, then n must be fothe form (Where k is an integer)

Options

A.4k +1
B.4k + 2
C.4k + 3
D.4k

Solution

       
Since, arg    
⇒    
∴     = (i)n ⇒ in = 1
Alternate Solution
Since,    arg
∴      
⇒    
⇒    
∴       z1and z2 are n th roots of unity
∴       z1n = z2n = 1
⇒    
∴       in = n
⇒     n = 4 k, where k is an integer

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