What is (sqrt(-4)+i)(6-5i) ?

The solution to (sqrt(-4)+i)(6-5i) is 15+18i

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simplify (sqrt(-4)+i)(6-5i)

simplify

(- 4 + i) (6 - 5 i)

15 + 18 i

Solution steps

(- 4 + i) (6 - 5 i)

Apply complex arithmetic rule:

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

= (- 4 \cdot 6 - 1 \cdot (- 5)) + (- 4 (- 5) + 1 \cdot 6) i

Simplify

(- 4 \cdot 6 - 1 \cdot (- 5)) + (- 4 (- 5) + 1 \cdot 6) i : (12 i + 5) + (- 10 i + 6) i

= (12 i + 5) + (- 10 i + 6) i

Simplify

(12 i + 5) + (- 10 i + 6) i : 18 i + 15

= 18 i + 15

Rewrite in standard complex form:

15 + 18 i

= 15 + 18 i

44 x + 20 x^{2} - 15

- 64 \div 8

\frac{1}{9} + \frac{1}{4}

2^{- 9} \cdot 4^{3}

\frac{5}{3} \div 2