Find the sum. Express your answer in standard form. 5 ( 4 + 7 i ) + 6 ( 3 − 2 i ) 5\left(4+7i\right)+6\left(3-2i\right) 5 ( 4 + 7 i ) + 6 ( 3 − 2 i )

Hey, everyone. Let's take a look at this practice problem. So I wanna find the sum of these two complex numbers and express my answer in standard form. So here I have 5 times 4+7i+6 times 3 minus 2i. So let's go ahead and get rid of those parentheses. Now I actually have coefficients on the outside of both of these complex numbers, so that means I need to go ahead and distribute that in before I go any further. So for my first term, I have 4 5 times 4, which is going to give me 20, and then 5 times 7 I, I, which is going to give me 35 I. Then I have positive 6 multiplying my 3, which is going to give me a positive 18. And then lastly, I have 6 times negative 2 I, which is gonna give me a negative 12 I. Now I can go ahead and combine like terms. So I have my 20 and my 18, which are gonna combine to give me positive 38. And then I have my 35 I and then my minus 12 I, which is going to give me a positive 23 I. Now checking that my answer is in standard form, a+bi, and it is. So my final answer is 38 +23i. Let me know if you have any questions.

1. Equations and Inequalities

Complex Numbers

Precalculus

1. Equations and Inequalities

Complex Numbers

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Multiple Choice

Find the sum. Express your answer in standard form. $5\left(4+7i\right)+6\left(3-2i\right)$

$7+5i$

$38+23i$

$2+47i$

$7+9i$

Verified step by step guidance

First, distribute the 5 into the expression (4 + 7i). This means you multiply 5 by each term inside the parentheses: 5 * 4 and 5 * 7i.

Next, distribute the 6 into the expression (3 - 2i). This involves multiplying 6 by each term inside the parentheses: 6 * 3 and 6 * -2i.

After distributing, you will have two complex numbers. Add these two complex numbers together by combining the real parts and the imaginary parts separately.

Now, add the result from the previous step to the complex number (7 + 5i). Again, combine the real parts and the imaginary parts separately.

Finally, express the sum in standard form, which is a + bi, where a is the real part and b is the imaginary part.

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Struggling with Precalculus?

Find the sum. Express your answer in standard form. 5(4+7i)+6(3−2i)5\left(4+7i\right)+6\left(3-2i\right)5(4+7i)+6(3−2i)

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Find the sum. Express your answer in standard form. $5\left(4+7i\right)+6\left(3-2i\right)$