How do you simplify $(1+3i) div (5-3i)$ ?

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Answer 1 · 2015-11-22T02:35:42

$-1/9+1/2i$

Write as $(1+3i)/(5-3i)$ . Multiply by the complex conjugate of the denominator.

$(1+3i)/(5-3i)((5+3i)/(5+3i))=(5+3i+15i+9i^2)/(25cancel(-15i+15i)-9i^2)=(5+18i+9i^2)/(25-9i^2)$

Recall that $i=sqrt(-1)$ , so $color(red)(i^2=-1$ .

$(5+18i+9(-1))/(25-9(-1))=(-4+18i)/36=-1/9+1/2i$

Note that the answer is written in the $a+bi$ form of a complex number.

How do you simplify (1+3i) div (5-3i) (1+3i) div (5-3i) ?