Question

Solve step by step :
(2+2i)(5+3i)

Answer 1

`\displaystyle 4+16i`

Explanation:

Distributive property: ⇒ A(B+C)=AB+AC

A=2, B=2, C=5, and D=3

`\displaystyle (2*5-2*3)+(2*3+2*5)i`

Simplify and refine to find the answer.

`\displaystyle2*3+2*5=2*3=6, 2*5=10, 10+6=16`

`\displaystyle2*5-2*3=2*5=10-2*3=2*3=6, 10-6=4`

`\displaystyle 4+16i` , which is our correct answer.

Answer 2

(2 + 2i)(5 + 3i) = 4 + 16i

Explanation:

Use FOIL: (a + b)(c + d) = ac + ad + bc + bd

and i² = -1

(2 + 2i)(5 + 3i) = (2)(5) + (2)(3i) + (2i)(5) + (2i)(3i)

= 10 + 6i + 10i + 6i² = 10 + 6i + 10i + 6(-1)

= 10 + 6i + 10i - 6 combine like terms

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

= 4 + 16i