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

The solution to 2(1+3i)-3/2 (-2+i) is 5+9/2 i

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

simplify

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

5 + \frac{9}{2} i

Solution steps

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

Expand

2 (1 + 3 i) : 2 + 6 i

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

Expand

- \frac{3}{2} (- 2 + i) : 3 - \frac{3}{2} i

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

Group like terms

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

Add the numbers:

2 + 3 = 5

= 6 i - \frac{3}{2} i + 5

Factor out common term

i

= i (6 - \frac{3}{2}) + 5

6 - \frac{3}{2} = \frac{9}{2}

= i \frac{9}{2} + 5

Rewrite in standard complex form:

5 + \frac{9}{2} i

= 5 + \frac{9}{2} i

2 (2 x - \frac{1}{2}) = \frac{1}{7} (1 - \frac{x}{2})

π (12)^{2}

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