What is (2+4i)/(1-i)+2i(3-i) ?

The solution to (2+4i)/(1-i)+2i(3-i) is 1+9i

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simplify (2+4i)/(1-i)+2i(3-i)

simplify

\frac{2 + 4 i}{1 - i} + 2 i (3 - i)

1 + 9 i

Solution steps

\frac{2 + 4 i}{1 - i} + 2 i (3 - i)

Simplify

\frac{2 + 4 i}{1 - i} : \frac{- 2 + 6 i}{2}

= \frac{- 2 + 6 i}{2} + 2 i (3 - i)

Expand

2 i (3 - i) : 6 i + 2

= \frac{- 2 + 6 i}{2} + 6 i + 2

Cancel

\frac{- 2 + 6 i}{2} : - 1 + 3 i

= - 1 + 3 i + 6 i + 2

Group like terms

= 3 i + 6 i - 1 + 2

Add similar elements:

3 i + 6 i = 9 i

= 9 i - 1 + 2

Add the numbers:

- 1 + 2 = 1

= 9 i + 1

Rewrite in standard complex form:

1 + 9 i

= 1 + 9 i

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