Consider the two complex numbers z and w such that w=(z-1/z+2)=a+b i, where a, b ∈ R. Which of the following equals |z| ?

Question

Consider the two complex numbers z and w such that w=(z-1/z+2)=a+b i, where a, b ∈ R. Which of the following equals |z| ? (A) |w| (B) (a+1)2+b2 (C) a2+(b+2)2 (D) ( a +1)2+( b +1)2

Tardigrade Admin · Accepted Answer

Correct answer is (b) (a+1)2+b2

Q. Consider the two complex numbers $z$ and $w$ such that $w = \frac{z - 1}{z + 2} = a + bi$ , where $a, b \in R$ .
Which of the following equals $∣ z ∣$ ?

$∣ w ∣$

$(a + 1)^{2} + b^{2}$

$a^{2} + (b + 2)^{2}$

$(a + 1)^{2} + (b + 1)^{2}$

Correct answer is (b) $(a + 1)^{2} + b^{2}$

Q. Consider the two complex numbers z and w such that w=z+2z−1​=a+bi, where a,b∈R. Which of the following equals ∣z∣ ?

∣w∣

(a+1)2+b2

a2+(b+2)2

(a+1)2+(b+1)2