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What would say about module of complex numbers 1 + `sqrt3` *i and 1 - `sqrt3` *i?

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ruals | Salutatorian

Posted October 4, 2013 at 5:21 PM via web

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What would say about module of complex numbers 1 + `sqrt3` *i and 1 - `sqrt3` *i?

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sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted October 4, 2013 at 5:53 PM (Answer #1)

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You need to evaluate the absolute values of both complex numbers, using the following formula, such that:

`|z| = sqrt(x^2 + y^2)`

x represents the real part

y represents the imaginary part

Identifying the real and imaginary parts of the first complex number `z = 1 + sqrt3*i` , yields:

`x = 1, y = sqrt3 =>|z| = sqrt(1^2 + (sqrt3)^2) =>|z| = sqrt4 =>|z| = 2`

Identifying the real and imaginary parts of the next complex number `z = 1 - sqrt3*` i, yields:

`x = 1, y = -sqrt3 => |z| = sqrt(1^2 + (-sqrt3)^2) =>|z| = sqrt4 =>|z| = 2`

Hence, evaluating the absolute values of both given complex numbers yields that they have equal values, `|z| = 2` .

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