What is i(1-isqrt(3))(sqrt(3)+i) ?

The solution to i(1-isqrt(3))(sqrt(3)+i) is 2+2sqrt(3)i

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simplify i(1-isqrt(3))(sqrt(3)+i)

simplify

i (1 - i 3) (3 + i)

2 + 23 i

Solution steps

i (1 - i 3) (3 + i)

Rewrite

1 - i 3

in standard complex form:

1 - 3 i

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

Apply complex arithmetic rule:

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

= i ((1 \cdot 3 - (- 3) \cdot 1) + (1 \cdot 1 - 33) i)

Simplify

(1 \cdot 3 - (- 3) \cdot 1) + (1 \cdot 1 - 33) i : 23 - 2 i

= i (23 - 2 i)

Apply the distributive law:

a (b - c) = ab - a c

i (23 - 2 i) = i 23 - i 2 i

= i 23 - i 2 i

i 23 = 23 i

- i 2 i = 2

= 23 i + 2

Rewrite in standard complex form:

2 + 23 i

= 2 + 23 i

\frac{4}{8} + \frac{1}{4}

15 c^{2} d^{2} + 60 c^{2} d

\frac{x ^{2} + 5 x - 14}{2 - x}

(0.75)^{2}

(b + 4) (b - 2)

What is i(1-isqrt(3))(sqrt(3)+i) ?
The solution to i(1-isqrt(3))(sqrt(3)+i) is 2+2sqrt(3)i