Calculate: (5-2i) \times (2+3i)

Expression: $\left( 5-2i \right) \times \left( 2+3i \right)$

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

$5 \times 2+5 \times 3i-2i \times 2-2i \times 3i$

Multiply the numbers

$10+5 \times 3i-2i \times 2-2i \times 3i$

Calculate the product

$10+15i-2i \times 2-2i \times 3i$

Calculate the product

$10+15i-4i-2i \times 3i$

Calculate the product

$10+15i-4i-6{i}^{2}$

By definition ${i}^{2}=-1$

$10+15i-4i-6 \times \left( -1 \right)$

Any expression multiplied by $-1$ equals its opposite

$10+15i-4i+6$

Add the numbers

$16+15i-4i$

Collect like terms

$16+11i$