How do you simplify $(3+i)/(3-i)$ and write the complex number in standard form?

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Answer 1 · 2017-01-05T18:54:26

$4/5 +i 3/5$

Multiply the expression in the numerator and the denominator by the conjugate of the number in the denominator, to make the denominator a real number

$(3+i)/(3-i) * (3+i)/(3+i)$

= $(9+6i+i^2)/(9-i^2)$

= $(9+6i-1)/(9+1)$

= $(8+6i)/10$

= $8/10 +(6i)/10$

= $4/5 +i 3/5$

How do you simplify (3+i)/(3-i)(3+i)/(3-i) and write the complex number in standard form?