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Algebra Level 3

Which is the only complex number only represented by its magnitude ?

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The answer is 0.

A Former Brilliant Member by A Former Brilliant Member

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2 solutions

Vishnu Bhagyanath
Jul 12, 2015

Shouldn't it be all positive real numbers? Or did I make a mistake or misread the question?

∣ z ∣ = z | z | = z Let z = x + i y z = x+iy x 2 + y 2 = x + i y \sqrt{x^2 + y^2} = x+iy 2 y 2 = 0 2y^2=0 y = 0 y=0 x can take any value.

e.g. 5 + 0 i = 5 = ∣ 5 + 0 i ∣ = 5. 5+0i = 5 = |5+0i| = 5.

3 Helpful 0 Interesting 0 Brilliant 0 Confused

exactly! it should be all non negative reals!!

shuvam keshari - 5 years, 9 months ago

0 is a complex number (or rather it belongs to the set of complex number) since a + bi is a complex number even when a = b = 0.

0 Helpful 0 Interesting 0 Brilliant 0 Confused

Rather all the numbers on X-axis in complex plane will be represented by their magnitude.

abhishek Yadav - 2 years, 9 months ago

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