What is (2/3+1/2 i)(12-1/3 i) ?

The solution to (2/3+1/2 i)(12-1/3 i) is 49/6+52/9 i

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simplify (2/3+1/2 i)(12-1/3 i)

simplify

(\frac{2}{3} + \frac{1}{2} i) (12 - \frac{1}{3} i)

\frac{49}{6} + \frac{52}{9} i

Solution steps

(\frac{2}{3} + \frac{1}{2} i) (12 - \frac{1}{3} i)

Apply complex arithmetic rule:

(a + bi) (c + d i) = (a c - b d) + (a d + b c) i

= (\frac{2}{3} \cdot 12 - \frac{1}{2} (- \frac{1}{3})) + (\frac{2}{3} (- \frac{1}{3}) + \frac{1}{2} \cdot 12) i

Simplify

(\frac{2}{3} \cdot 12 - \frac{1}{2} (- \frac{1}{3})) + (\frac{2}{3} (- \frac{1}{3}) + \frac{1}{2} \cdot 12) i : \frac{49}{6} + \frac{52}{9} i

= \frac{49}{6} + \frac{52}{9} i

(x + 1)^{2} - (x + 1) - 6

\frac{5}{3 - 1}

16 i

\frac{x + 2}{x ^{3} + 8}

- ∣ - 3 ∣

What is (2/3+1/2 i)(12-1/3 i) ?
The solution to (2/3+1/2 i)(12-1/3 i) is 49/6+52/9 i