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 & Inequalities

Complex Numbers

College Algebra

1. Equations & 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

Distribute the 5 across the terms in the first complex number: $5(4 + 7i)$. This results in $5 \times 4 + 5 \times 7i$.

Distribute the 6 across the terms in the second complex number: $6(3 - 2i)$. This results in $6 \times 3 - 6 \times 2i$.

Add the real parts from the results of the distributions: $20 + 18$.

Add the imaginary parts from the results of the distributions: $35i - 12i$.

Combine the sums of the real and imaginary parts to express the final result in standard form: $38 + 23i$.

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Struggling with College Algebra?

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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Complex Numbers practice set

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