Question

Simplify the expression. Write the answer in standard form. (4-2i)(3-4i)

Answer 1

The simplified expression of (4-2i)(3-4i) is 4 - 22i. The process involves using the distributive property (FOIL method) and simplifying like terms, while remembering that i^2 equals -1.

Step-by-step explanation:

To simplify the expression (4-2i)(3-4i), we need to multiply the two complex numbers together. Use the distributive property, also known as the FOIL method for binomials:

• First, multiply the first terms: 4 × 3 = 12.
• Outer terms: 4 × -4i = -16i.
• Inner terms: -2i × 3 = -6i.
• Last terms: -2i × -4i = 8i².

Recall that i² = -1, so we can substitute this into the expression to simplify it further:

• 8i² = 8 × -1 = -8.

Now, combine like terms (real terms with real, imaginary terms with imaginary):

• 12 - 8 = 4 (real part).
• -16i - 6i = -22i (imaginary part).

Therefore, the simplified expression in standard form is: 4 - 22i.

To check if the answer is reasonable, ensure that all like terms have been combined and that the imaginary unit i has not been left squared without recalling that i² = -1. This will provide you the correct standard form of a complex number.