Find the difference. Express your answer in standard form. ( 2 + 8 i ) − ( 4 − i ) \left(2+8i\right)-\left(4-i\right) ( 2 + 8 i ) − ( 4 − i )

Hey, everyone. In this problem, I wanna find the difference between these two complex numbers. And here I have 2+8i minus 4 minus I. So the first thing I wanna do is get rid of all of these parentheses. So my first complex number is going to stay the same, 2+8i, and I can just get rid of those parentheses. Over the second one, I need to distribute my negative into it. So distributing that negative, I then have negative 4 and then negative negative I is going to give me positive I. And now I can just combine like terms. So I have 2 and negative 4 that are just both real numbers that I can go ahead and combine together, and 2 minus 4 is going to give me negative 2. Then I have 8 I and positive one so I can go ahead and combine these like terms as well. And 8i plus another I is going to give me a positive 9i. I wanna make sure that my answer in is in standard form, and it is. So my final answer is negative 2+9i. I'll see you in the next one.

1. Equations and Inequalities

Complex Numbers

Precalculus

1. Equations and Inequalities

Complex Numbers

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Multiple Choice

Find the difference. Express your answer in standard form. $\left(2+8i\right)-\left(4-i\right)$

$-2+9i$

$6+7i$

$2+7i$

$2-9i$

Verified step by step guidance

Identify the expression to simplify: (2 + 8i) - (4 - i).

Distribute the negative sign across the second complex number: (2 + 8i) - 4 + i.

Combine like terms by adding the real parts and the imaginary parts separately: (2 - 4) + (8i + i).

Simplify the real part: 2 - 4 = -2.

Simplify the imaginary part: 8i + i = 9i. Therefore, the expression simplifies to -2 + 9i.

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Struggling with Precalculus?

Find the difference. Express your answer in standard form. (2+8i)−(4−i)\left(2+8i\right)-\left(4-i\right)(2+8i)−(4−i)

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Find the difference. Express your answer in standard form. $\left(2+8i\right)-\left(4-i\right)$