What is (74)/(5-7i)+(15-20i)/(1-2i)-(10i)/(2-i) ?

The solution to (74)/(5-7i)+(15-20i)/(1-2i)-(10i)/(2-i) is 18+5i

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simplify (74)/(5-7i)+(15-20i)/(1-2i)-(10i)/(2-i)

simplify

\frac{74}{5 - 7 i} + \frac{15 - 20 i}{1 - 2 i} - \frac{10 i}{2 - i}

18 + 5 i

Solution steps

\frac{74}{5 - 7 i} + \frac{15 - 20 i}{1 - 2 i} - \frac{10 i}{2 - i}

\frac{74}{5 - 7 i} = 5 + 7 i

\frac{15 - 20 i}{1 - 2 i} = 11 + 2 i

\frac{10 i}{2 - i} = 4 i - 2

= 5 + 7 i + 11 + 2 i - (4 i - 2)

Expand

- (4 i - 2) : - 4 i + 2

= 5 + 7 i + 11 + 2 i - 4 i + 2

Group like terms

= 7 i + 2 i - 4 i + 5 + 11 + 2

Add similar elements:

7 i + 2 i - 4 i = 5 i

= 5 i + 5 + 11 + 2

Add the numbers:

5 + 11 + 2 = 18

= 5 i + 18

Rewrite in standard complex form:

18 + 5 i

= 18 + 5 i

\frac{2 + 2}{2}

I n^{1}

(x - 6) (x^{2} + 2 x - 4)

\frac{5}{4} + \frac{1}{5}

What is (74)/(5-7i)+(15-20i)/(1-2i)-(10i)/(2-i) ?
The solution to (74)/(5-7i)+(15-20i)/(1-2i)-(10i)/(2-i) is 18+5i