Find the product of 5 − 3 i and its conjugate. The answer is a + b i where

Question

math answer i need

Answer 1

The conjugate of 5 - 3i is 5 + 3i.  FOIL it out to find the product, remembering that i² = -1:

 

(5-3i)(5+3i) = 5·5 + 5·3i - 3i·5 + (-3i)(3i) = _____?

 

See a pattern?

Answer 2

The conjugate of a+bi is a-bi and vice versa:

 

The long way:

(5-3i)(5+3i)

= 5(5) + 5(3i) -3i(5) - 3i(3i)

= 25 - 9i²

= 25 - (9)(-1)

= 25 + 9

= 34

 

(a-bi)(a+bi)

= a² + abi - abi - b²i²

= a² + b²

 

From the formula:

(5-3i)(5+3i); a=5, b=3

a²+b² = 5² + 3² = 34