Question

Simplify the expression to a bi form: left bracket, 5, minus, 8, i, right bracket, left bracket, 8, minus, 6, i, right bracket (5−8i)(8−6i)

Answer 1

To simplify (5-8i)(8-6i), use the FOIL method to expand the product and combine like terms, resulting in the simplified bi form of (-8 - 94i).

Step-by-step explanation:

To simplify the expression (5-8i)(8-6i) to a bi form, we will use the distributive property (also known as the FOIL method in this context) to expand the product of these two complex numbers.

• Multiply the real parts: 5 × 8 = 40.
• Multiply the outside terms: 5 × (-6i) = -30i.
• Multiply the inside terms: (-8i) × 8 = -64i.
• Multiply the imaginary parts: (-8i) × (-6i) = +48i². Remember that i² = -1.

Add all four products together: 40 - 30i - 64i + 48i². Since i² = -1, the term 48i² becomes 48(-1), or -48.

Combine like terms: 40 - 48 and -30i - 64i.

The final simplified form in a bi form is (-8 - 94i).