Perform the indicated operation. Express your answer in standard form. (3+8i)2\left(3+8i\right)^2(3+8i)2

− 55 + 48 i -55+48i − 55 + 48 i

Perform the indicated operation. Express your answer in standard form. ( 3 + 8 i ) 2 \left(3+8i\right)^2 ( 3 + 8 i ) 2

Hey, everyone. Let's take a look at this practice problem. So here, I wanna perform the indicated operation and then express my answer in standard form, And I have 3 +8i squared. Now whenever something is squared, that just means it's being multiplied by itself. So this is really just 3 +8i times 3+8i, and then I can go ahead and start my steps for multiplying complex numbers. So starting with step 1, I either want to distribute or foil. And in this case, since I have 2 complex numbers with 2 terms each, I want to foil. So let's go ahead and start foiling here. Starting with my first term, I have 3 times 3, which gives me 9. Then my outside terms, 3 times 8 I gives me a positive 24 I. Then my inside terms, I have an 8 I times the 3 again, which is positive 24 I. And then my last terms, 8 I times 8 I is going to give me positive 64i squared. Now step 1 is done. I can move on to step 2, which is to apply I squared equals negative one. So I have my I squared term here, so I need to go ahead and take this 64 I squared. This becomes 64 times negative one since I squared is negative 1, and then 64 times negative one is just negative 64. Now I can just bring all of my other terms down. So I can bring this 9 down and then both of my I terms, which happen to be both 24 I. And then I have simplified it to to now I can move on to step 3. So step 2 is done. Now I just need to combine all of my like terms. So I have this 9 and this negative 64 that are both constants that combine to give me negative 55. And then I have both of my I terms, which are going to combine 24 I plus 24 I gives me positive 48 I. Now I, of course, want to check after I have completed step 3 that my answer is in standard form and standard form is a+bi and that is exactly the form that I have here. So this is my final answer, negative 55 +48i. That's all for this one. I'll see you in the next one.

Perform the indicated operation. Express your answer in standard form. ( 3 + 8 i ) 2 \left(3+8i\right)^2 ( 3 + 8 i ) 2

− 55 + 48 i -55+48i − 55 + 48 i

1. Equations and Inequalities

Complex Numbers

Precalculus

1. Equations and Inequalities

Complex Numbers

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Multiple Choice

Perform the indicated operation. Express your answer in standard form. $\left(3+8i\right)^2$

$-55+48i$

$9+64i$

$24i$

$9+24i$

Verified step by step guidance

Start by recognizing that you need to square the complex number (3 + 8i). This means you will multiply (3 + 8i) by itself.

Apply the formula for squaring a binomial: (a + b)^2 = a^2 + 2ab + b^2. Here, a = 3 and b = 8i.

Calculate a^2: (3)^2 = 9.

Calculate 2ab: 2 * 3 * 8i = 48i.

Calculate b^2: (8i)^2 = 64i^2. Remember that i^2 = -1, so 64i^2 = 64 * (-1) = -64.

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