Simple-complex ;-)

Algebra Level 3

The Complex Number Z satisfies Z + ∣ Z ∣ = 2 + 8 i Z + |Z| = 2 + 8i What is the Value of |Z| ?


The answer is 17.

Ayush Parasar by Ayush Parasar , 22, India

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1 solution

Aareyan Manzoor
Oct 19, 2015

let Z = a + b Z = a+b then a + a 2 + b 2 + b i = 2 + 8 i a+\sqrt{a^2+b^2}+bi=2+8i b = 8 b=8 a + a 2 + 64 = 2 ⟹ a = − 15 a+\sqrt{a^2+64}=2\Longrightarrow a=-15 ∣ z ∣ = ( − 15 ) 2 + 8 2 = 17 |z|=\sqrt{(-15)^2 +8^2}=\boxed{17}

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