What is i(4-2i)(5+2i) ?

The solution to i(4-2i)(5+2i) is 2+24i

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simplify i(4-2i)(5+2i)

simplify

i (4 - 2 i) (5 + 2 i)

2 + 24 i

Solution steps

i (4 - 2 i) (5 + 2 i)

Apply complex arithmetic rule:

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

= i ((4 \cdot 5 - (- 2) \cdot 2) + (4 \cdot 2 - 2 \cdot 5) i)

Simplify

(4 \cdot 5 - (- 2) \cdot 2) + (4 \cdot 2 - 2 \cdot 5) i : 24 - 2 i

= i (24 - 2 i)

Apply the distributive law:

a (b - c) = ab - a c

i (24 - 2 i) = i 24 - i 2 i

= i 24 - i 2 i

i 24 = 24 i

- i 2 i = 2

= 24 i + 2

Rewrite in standard complex form:

2 + 24 i

= 2 + 24 i

(- 5 + 7 i) - (- 11 + 2 i)

60 \times \frac{1}{4}

(5 y^{2} - z)^{5}

7 x + x^{2}