“BeMath“ Let the complex number z satisfies the equation 3(z−1)= i(z+1) (1) find z in the form a+bi where a,b ∈R (2) find the value of ∣z∣ and ∣z−z^∗ ∣


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Question Number 107690 by bemath last updated on 12/Aug/20

$‘ ‘ B e M a t h ‘ ‘$ $L e t t h e c o m p l e x n u m b e r z s a t i s f i e s t h e$ $e q u a t i o n 3 (z - 1) = i (z + 1)$ $(1) f i n d z i n t h e f o r m a + b i w h e r e a, b \in R$ $(2) f i n d t h e v a l u e o f ∣ z ∣ a n d ∣ z - z^{*} ∣$
	Answered by mr W last updated on 12/Aug/20

	$(1)$ $z = a + b i$ $3 (a + b i - 1) = i (a + b i + 1)$ $(3 a - 3) + 3 b i = - b + (a + 1) i$ $3 a - 3 = - b \Rightarrow 3 a + b = 3$ $3 b = a + 1 \Rightarrow a - 3 b = - 1$ $9 a + 3 b = 9$ $\Rightarrow a = \frac{4}{5}$ $\Rightarrow b = \frac{3}{5}$
	Commented by bemath last updated on 12/Aug/20

	$∣ z ∣= \sqrt{\frac{16}{25} + \frac{9}{25}} = 1 . i t c o r r e c t ?$
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