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Find the set of complex numbers z satisfying the two conditions: Re ( ( z +1) 2 =0 and ( z +1) 2 =2 i. Here Re ( a + bi ) = a if both a, b ∈ R . Then find the cardinality of the set.

Find the set of complex numbers z satisfying the two conditions:

Re((z+1)2=0 and (z+1)2 =2i. Here Re(a + bi) = a if both a, b ∈ R.

Then find the cardinality of the set.

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Grade:12

1 Answers

Aditya Gupta
2081 Points
4 years ago
dear student, this is an extremely ez ques.
note that in the condition (z+1)2 =2i if we take Re part both sides, we get
Re((z+1)2= Re(2i)= 0
hence, (z+1)2 =2i itself implies the truth of the 2nd condition Re((z+1)2= 0.
so, we only need to be concerned with solving (z+1)2 =2i
but, we know that 2i= (1+i)^2
so,  (z+1)2 = (i+1)^2
or z+1= ± (i+1)
or z= i, – (i+2)
the cardinality of set means the no. of elements in the set, which in this case is clearly 2.
KINDLY APPROVE :))

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