Simplify (4 + 7i)(3 + 4i)?

We will use the concept of multiplication of complex numbers.

Answer: We can write the simplified form of (4 + 7i) (3 + 4i) as (-16 + 37i).

Let us proceed step by step

Explanation:

We will express the product (4 + 7i) (3 + 4i) in the form of a + ib, where a is a real number and b is an imaginary number.

Use the distributive property to multiply the complex numbers.

(4 + 7i) (3 + 4i) = 4 × (3 + 4i) +  7i × (3 + 4i)

= 12 + 16i + 21i + 28i²

= 12 + 37i + 28(-1). [ As we know that i = √-1 and i² = -1]

= 12 - 28 +37i

= -16 + 37i

Therefore, we can write the simplified form of (4 + 7i) (3 + 4i) as (-16 + 37i).