What is modulus of z = 1 - 2i?

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sciencesolve | Teacher | (Level 3) Educator Emeritus

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You need to evaluate the absolute value of the given complex number, using the following formula, such that:

`|z| = sqrt(x^2 + y^2)`

Identifying the real part x and the imaginary part y, yields:

`{(x = 1),(y = -2):}`

Reasoning by analogy, yields:

`|z| = sqrt(1^2 + (-2)^2)`

`|z| = sqrt(1 + 4)`

`|z| = sqrt 5`

Hence, evaluating the absolute value of the given complex number, yields `|z| = sqrt 5.`

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tonys538 | Student, Undergraduate | (Level 1) Valedictorian

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The modulus of a complex number x + i*y is given by `sqrt(x^2 + y^2)`

For the complex number z = 1 - 2i, the equivalent values of x and y are 1 and -2 respectively.

The modulus of the complex number is `sqrt(1^2 + (-2)^2)` = `sqrt(1 + 4)` = `sqrt 5`

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