What is (3i)(-3-4i)(7-5i) ?

The solution to (3i)(-3-4i)(7-5i) is 39-123i

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simplify (3i)(-3-4i)(7-5i)

simplify

(3 i) (- 3 - 4 i) (7 - 5 i)

39 - 123 i

Solution steps

(3 i) (- 3 - 4 i) (7 - 5 i)

Apply complex arithmetic rule:

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

= 3 i ((- 3 \cdot 7 - (- 4) (- 5)) + (- 3 (- 5) - 4 \cdot 7) i)

Simplify

(- 3 \cdot 7 - (- 4) (- 5)) + (- 3 (- 5) - 4 \cdot 7) i : - 41 - 13 i

= 3 i (- 41 - 13 i)

Apply the distributive law:

a (b - c) = ab - a c

3 i (- 41 - 13 i) = 3 i (- 41) - 3 i 13 i

= 3 i (- 41) - 3 i 13 i

3 i (- 41) = - 123 i

- 3 i 13 i = 39

= - 123 i + 39

Rewrite in standard complex form:

39 - 123 i

= 39 - 123 i

\frac{7}{20} + \frac{7}{16}

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

(5 x + 6) (x + 4)

(2 \cdot 1 0^{5})^{3}

(- 3 x^{2} + 10) - (- 2 x^{2} + 2)