Question

(2+3i).(2+5i) what is the answer for this

Answer 1

Answer:

-11+16i

Step by step explanation:

(2+3i).(2+5)

Multiply each term in the first parentheses by each term in the second parentheses(FOIL)

2x2+2x5i+3ix2+3ix5i

Multiply the numbers

4+2x5+3ix2+3ix5i

Calculate the product

4+10i+3ix2+3ix5i

Calculate the product

4+10i+6i+3ix5i

Calculate the product

4+10i+6i+15i^2

By definition i^2=-1

4+10i+6i+15x(-1)

Any expression multiplied by -1 equals its opposite

4+10i+6i-15

Calculate the difference

-11+10i+6i

Collect like terms

-11+16i

Answer 2

-11 + 16i

Explanation:

Multiply out the expression just as you would for any two binomials (FOIL), keeping in mind that i^2 = -1.

(2 + 3i)(2 + 5i) = 4 + 10i + 6i + 15i^2 = 4 + 10i + 6i +15(-1)

Combine like terms; "plain numbers" together and i terms together.

(4 - 15) + (10+6)i = -11 + 16i