What is 2(1-i)^2+3(-2+4i)-5(sqrt(3)-2i)^2 ?

The solution to 2(1-i)^2+3(-2+4i)-5(sqrt(3)-2i)^2 is -1+4(2+5sqrt(3))i

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simplify 2(1-i)^2+3(-2+4i)-5(sqrt(3)-2i)^2

simplify

2 (1 - i)^{2} + 3 (- 2 + 4 i) - 5 (3 - 2 i)^{2}

- 1 + 4 (2 + 53) i

Solution steps

2 (1 - i)^{2} + 3 (- 2 + 4 i) - 5 (3 - 2 i)^{2}

2 (1 - i)^{2} = - 4 i

(3 - 2 i)^{2} = - 43 i - 1

= - 4 i + 3 (- 2 + 4 i) - 5 (- 43 i - 1)

Expand

3 (- 2 + 4 i) : - 6 + 12 i

= - 4 i - 6 + 12 i - 5 (- 43 i - 1)

Expand

- 5 (- 43 i - 1) : 203 i + 5

= - 4 i - 6 + 12 i + 203 i + 5

Group like terms

= - 4 i + 12 i + 203 i - 6 + 5

Add similar elements:

- 4 i + 12 i = 8 i

= 8 i + 203 i - 6 + 5

Add the numbers:

- 6 + 5 = - 1

= 8 i + 203 i - 1

Factor out common term

4 i : 4 i (2 + 53)

= 4 i (2 + 53) - 1

Rewrite in standard complex form:

- 1 + 4 (2 + 53) i

= - 1 + 4 (2 + 53) i

Expand

4 (2 + 53) : 8 + 203

= - 1 + (8 + 203) i

Expand

- 1 + (8 + 203) i : - 1 + 4 i (2 + 53)

= - 1 + 4 i (2 + 53)

Rewrite in standard complex form:

- 1 + 4 (2 + 53) i

= - 1 + 4 (2 + 53) i

\frac{π ( 0.05 ) ^{2}}{4}

\frac{4}{2 + 3}

\frac{1 - sin ^{2} ( x )}{cos ( x )}

- 4 \cdot (- 9)

23 \cdot 5

What is 2(1-i)^2+3(-2+4i)-5(sqrt(3)-2i)^2 ?
The solution to 2(1-i)^2+3(-2+4i)-5(sqrt(3)-2i)^2 is -1+4(2+5sqrt(3))i