JEE Main20248 Apr 2024Morning ShiftMathematicsComplex NumberActual

Let z be a complex number such that |z+2|=1 and Im ( z+1 z+2 )= 1 5 . Then the value of | Re ( z+2 )| is

Options

A2 6 5
B24 5
C1+ 6 5
D6 5

Correct answer

A. 2 6 5

Step-by-step solution

|z+2|=1, Im ( z+1 z+2 )= 1 5 Let z+2= +i aligned & 1 z+2 = -i & z+1 z+2 =1- 1 z+2 =1-( -i ) & =(1- )+ isin & Im ( z+1 z+2 )= , = 1 5 & = 1- 1 25 = 2 6 5 & | Re ( z+2 )|= 2 6 5 aligned

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