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

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 I, 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.

11. Roots, Radicals, and Complex Numbers

Introduction to Complex Numbers

Beginning & Intermediate Algebra

11. Roots, Radicals, and Complex Numbers

Introduction to Complex Numbers

Struggling with Beginning & Intermediate Algebra?

Join thousands of students who trust us to help them ace their exams!Watch the first video

Multiple Choice

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

$-2+9i$

$6+7i$

$2+7i$

$2-9i$

Verified step by step guidance

Identify the complex numbers involved in the subtraction: the first complex number is $\left(2 + 8i\right)$ and the second complex number is $\left(4 - i\right)$.

Rewrite the expression to clearly show the subtraction of the two complex numbers: $\left(2 + 8i\right) - \left(4 - i\right)$.

Distribute the subtraction sign across the second complex number, changing the signs inside the parentheses: \$2 + 8i - 4 + i$.

Group the real parts together and the imaginary parts together: $(2 - 4) + (8i + i)$.

Simplify each group by performing the arithmetic operations: subtract the real parts and add the imaginary parts to express the result in standard form $a + bi$.

5:02m

Watch next

Master Square Roots of Negative Numbers with a bite sized video explanation from Patrick Ford

Start learning

Struggling with Beginning & Intermediate Algebra?

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

Watch next

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