Question

Jamal is doing electronics engineering research and determines the result of his analysis can be expressed in terms of Complex Numbers. His result is (8-4i) (5i-2) - (3-i). Jamal simplified this expression but doesn’t trust his result. Will you help him by simplifying this complex expression? For 5 points each: Explain in your own words the value of "i" and the value of i². (short answers please) Copy the problem carefully and show all the steps needed to arrive at the simplified answer for the multiplication part of the problem. You must show all your work for full credit. (8-4i)(5i-2) = Calculate the result of this when combined with the final complex term. Write your final, simplified expression in standard complex number form for Jamal.

Answer 1

To simplify the complex expression (8-4i)(5i-2) - (3-i), the multiplication is performed first resulting in 48i + 4. Then, the final complex term is subtracted, resulting in the simplified expression 1 + 49i.

Step-by-step explanation:

The value of i is the square root of -1, which is an imaginary number. The value of i squared, i2, is -1. To simplify Jamal's complex expression (8-4i)(5i-2) - (3-i), we first perform the multiplication:

• 8(5i) - 8(2) - 4i(5i) + 4i(2)
• 40i - 16 - 20i2 + 8i
• Since i2 = -1, this simplifies to 40i - 16 - 20(-1) + 8i.
• 40i + 8i + 20 - 16
• 48i + 4

Next, we subtract the final complex term (3-i):

• (48i + 4) - (3 - i)
• 48i + i + 4 - 3
• 49i + 1

The simplified expression in standard complex number form for Jamal is 1 + 49i.