What is (5+2i)(10i-5) ?

The solution to (5+2i)(10i-5) is -45+40i

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simplify (5+2i)(10i-5)

simplify

(5 + 2 i) (10 i - 5)

- 45 + 40 i

Solution steps

(5 + 2 i) (10 i - 5)

Rewrite

10 i - 5

in standard complex form:

- 5 + 10 i

= (5 + 2 i) (- 5 + 10 i)

Apply complex arithmetic rule:

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

= (5 (- 5) - 2 \cdot 10) + (5 \cdot 10 + 2 (- 5)) i

Simplify

(5 (- 5) - 2 \cdot 10) + (5 \cdot 10 + 2 (- 5)) i : - 45 + 40 i

= - 45 + 40 i

(\frac{c ^{- 4}}{81 d ^{8}})^{\frac{3}{4}}

1020 n^{4}

5 \cdot 36

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