For-z-a-bi-If-z-z-z-z-4bi-Find-z-

Question Number 204583 by hardmath last updated on 22/Feb/24

For z = a - bi

If (∣ z ∣ - z) \cdot (∣ z ∣ + \overset{―}{z}) = 4 bi

Find ∣ z ∣ = ?

Answered by A5T last updated on 22/Feb/24

(∣ z ∣ - z) (∣ z ∣ + \bar{z}) =∣ z ∣^{2} + \bar{z} ∣ z ∣ - z ∣ z ∣ - z \bar{z}

=∣ z ∣ (\bar{z} - z) = 4 b i \Rightarrow∣ z ∣= \frac{4 b i}{a + b i - (a - b i)} = 2

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