Multiply Complex Numbers 1

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Precalculus

Complex Numbers

Multiply Complex Numbers

Multiply Complex Numbers 1

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Question 1 of 5

1. Question
Solve

$i (5 + i)$ $i(5+i)$
- 1. $5 i - 1$ $5i-1$
- 2. $5 i + 1$ $5i+1$
- 3. $- 5 i + 1$ $-5i+1$
- 4. $- 5 i - 1$ $-5i-1$
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Imaginary numbers have the properties $i = \sqrt{- 1}$ $i=sqrt(-1)$ or $i^{2} = - 1$ $i^2=-1$ .

To solve $i (5 + i)$ $i(5+i)$ , multiply and then simplify.

$i (5 + i)$ $color(royalblue)(i)(5+i)$ Multiply the $i$ $i$ through the parentheses.

$=$ $=$ $5 i + i^{2}$ $5i+i^2$ Replace $i^{2} = - 1$ $i^2=-1$ .

$=$ $=$ $5 i - 1$ $5i-1$

$5 i - 1$ $5i-1$

Question 2 of 5

Solve

$(7 + i) (9 + i)$ $(7+i)(9+i)$

1. $64 + 16 i$ $64+16i$
2. $31 + 8 i$ $31+8i$
3. $62 + 16 i$ $62+16i$
4. $4 + i$ $4+i$

Question 3 of 5

Solve

$- 12 i (5 + 3 i)$ $-12i(5+3i)$

1. $36 + 60 i$ $36+60i$
2. $- 36 + 60 i$ $-36+60i$
3. $36 - 60 i$ $36-60i$
4. $- 36 - 60 i$ $-36-60i$

Question 4 of 5

Solve

$(- 1 + 4 i) (13 - i)$ $(-1+4i)(13-i)$

1. $9 - 53 i$ $9-53i$
2. $- 9 - 53 i$ $-9-53i$
3. $9 + 53 i$ $9+53i$
4. $- 9 + 53 i$ $-9+53i$

Question 5 of 5

Solve

${(5 + 11 i)}^{2}$ $(5+11i)^2$

1. $96 - 110 i$ $96-110i$
2. $- 96 - 110 i$ $-96-110i$
3. $96 + 110 i$ $96+110i$
4. $- 96 + 110 i$ $-96+110i$

	${(5 + 11 i)}^{2}$ $(5+11i)^2$	Expand ${(5 + 11 i)}^{2}$ $(5+11i)^2$ .
	$(5 + 11 i) (5 + 11 i)$ $(5+11i)(5+11i)$	Multiply using the FOIL method.
$=$ $=$	$25 + 55 i + 55 i + 121 i^{2}$ $25+color(red)(55i)+color(red)(55i)+121i^2$	Combine like terms $55 i$ $55i$ and $55 i$ $55i$ .
$=$ $=$	$25 + 110 i + 121 i^{2}$ $25+color(red)(110i)+121i^2$	Replace $i^{2} = - 1$ $i^2=-1$ .
$=$ $=$	$25 + 110 i - 121$ $25+110i-121$	Combine like terms $63$ $63$ and $- 1$ $-1$ .
$=$ $=$	$- 96 + 110 i$ $-96+110i$

Multiply Complex Numbers 1

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3. Question

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Quizzes

	$i (5 + i)$ $color(royalblue)(i)(5+i)$	Multiply the $i$ $i$ through the parentheses.
$=$ $=$	$5 i + i^{2}$ $5i+i^2$	Replace $i^{2} = - 1$ $i^2=-1$ .
$=$ $=$	$5 i - 1$ $5i-1$

	$- 12 i (5 + 3 i)$ $color(royalblue)(-12i)(5+3i)$	Multiply the $i$ $i$ through the parentheses.
$=$ $=$	$- 60 i - 36 i^{2}$ $-60i-36i^2$	Replace $i^{2} = - 1$ $i^2=-1$ .
$=$ $=$	$- 60 i + 36$ $-60i+36$	Rearrange.
$=$ $=$	$36 - 60 i$ $36-60i$

	$(- 1 + 4 i) (13 - i)$ $(-1+4i)(13-i)$	Multiply by foil.
$=$ $=$	$- 13 + i + 52 i - 4 i^{2}$ $-13+color(red)(i)+color(red)(52i)-4i^2$	Combine like terms $i$ $i$ and $52 i$ $52i$ .
$=$ $=$	$- 13 + 53 i - 4 i^{2}$ $-13+color(red)(53i)-4i^2$	Replace $i^{2} = - 1$ $i^2=-1$ .
$=$ $=$	$- 13 + 53 i + 4$ $-13+53i+4$	Combine like terms $- 13$ $-13$ and $4$ $4$ .
$=$ $=$	$- 9 + 53 i$ $-9+53i$