How do you write the following expression in standard form $(1+i)/i-3/(4-i)$ ?

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Answer 1 · 2016-10-22T12:14:21

The standard form is $5/17-(20i)/17$

le $z=(1+i)/i-3/(4-i)$

Reducing to the same denominator

$z=((1+i)(4-i)-3i)/(i(4-i))$

Recall that $i^2=-1$

Then $z=(4+3i-i^2-3i)/(4i-i^2)=5/(1+4i)$

We simplify further by multiplying by the conjugate of the denominator $1-4i$

$z=(5*(1-4i))/((1+4i)(1-4i))=(5-20i)/(1-16i^2)=(5-20i)/17$

$z=5/17-(20i)/17$

How do you write the following expression in standard form (1+i)/i-3/(4-i)(1+i)/i-3/(4-i)?