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

The solution to i(2+3i)(4i-1) is -5-14i

Popular >

simplify i(2+3i)(4i-1)

simplify

i (2 + 3 i) (4 i - 1)

- 5 - 14 i

Solution steps

i (2 + 3 i) (4 i - 1)

Rewrite

4 i - 1

in standard complex form:

- 1 + 4 i

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

Apply complex arithmetic rule:

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

= i ((2 (- 1) - 3 \cdot 4) + (2 \cdot 4 + 3 (- 1)) i)

Simplify

(2 (- 1) - 3 \cdot 4) + (2 \cdot 4 + 3 (- 1)) i : - 14 + 5 i

= i (- 14 + 5 i)

Apply the distributive law:

a (b + c) = ab + a c

i (- 14 + 5 i) = i (- 14) + i 5 i

= i (- 14) + i 5 i

i (- 14) = - 14 i

i 5 i = - 5

= - 14 i - 5

Rewrite in standard complex form:

- 5 - 14 i

= - 5 - 14 i

5 m p^{2} - m p

sin^{2} (x) + cos^{2} (x) + tan^{2} (x)

(x + 5) (x^{2} - 5 x + 25) - (x - 5) (x^{2} + 5 x + 25)

\frac{x ^{2} - x y}{x - y}