Multiply Complex Numbers 2

Topics

Precalculus

Complex Numbers

Multiply Complex Numbers

Multiply Complex Numbers 2

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Question 1 of 5

Solve

${(13 - 6 i)}^{2}$ $(13-6i)^2$

1. $133 - 156 i$ $133-156i$
2. $133 + 156 i$ $133+156i$
3. $- 133 - 156 i$ $-133-156i$
4. $- 133 + 156 i$ $-133+156i$

Question 2 of 5

Solve

${(3 - 4 i)}^{2}$ $(3-4i)^2$

1. $7 - 24 i$ $7-24i$
2. $7 + 24 i$ $7+24i$
3. $- 7 + 24 i$ $-7+24i$
4. $- 7 - 24 i$ $-7-24i$

Question 3 of 5

Solve

$(6 - 6 i) (7 - 6 i)$ $(6-6i)(7-6i)$

1. $- 6 + 78 i$ $-6+78i$
2. $- 6 - 78 i$ $-6-78i$
3. $6 + 78 i$ $6+78i$
4. $6 - 78 i$ $6-78i$

Question 4 of 5

Solve

$(-4-5i)^2$

1. $-9+40i$
2. $9+40i$
3. $-9-40i$
4. $9-40i$

Question 5 of 5

Solve

$(-2-3i)(-5+8i)$

1. $34-i$
2. $34+i$
3. $-34-i$
4. $-34+i$

	${(13 - 6 i)}^{2}$ $(13-6i)^2$	Expand ${(13 - 6 i)}^{2}$ $(13-6i)^2$ .
	$13^{2} + 2 \times 13 \times (- 6 i) + {(- 6 i)}^{2}$ $13^2+2times13times(-6i)+(-6i)^2$	Take the square of ${(- 6 i)}^{2}$ $(-6i)^2$ and $13^{2}$ $13^2$ .
$=$ $=$	$169 + 2 \times 13 \times (- 6 i) + 36 i^{2}$ $169+2times13times(-6i)+36i^2$	Multiply $2 \times 13 \times (- 6 i)$ $2times13times(-6i)$ .
$=$ $=$	$169 - 156 i + 36 i^{2}$ $169-156i+36i^2$	Replace $i^{2} = - 1$ $i^2=-1$ .
$=$ $=$	$169 - 156 i - 36$ $169-156i-36$	Combine like terms $63$ $63$ and $- 1$ $-1$ .
$=$ $=$	$133 - 156 i$ $133-156i$

	${(3 - 4 i)}^{2}$ $(3-4i)^2$	Expand ${(3 - 4 i)}^{2}$ $(3-4i)^2$ .
	$(3 - 4 i) (3 - 4 i)$ $(3-4i)(3-4i)$	Multiply using the FOIL method.
$=$ $=$	$9 - 12 i - 12 i + 16 i^{2}$ $9 color(red)(-12i) color(red)(-12i)+16i^2$	Combine like terms $- 12 i$ $-12i$ and $- 12 i$ $-12i$ .
$=$ $=$	$9 - 24 i + 16 i^{2}$ $9 color(red)(-24i)+16i^2$	Replace $i^{2} = - 1$ $i^2=-1$ .
$=$ $=$	$9 - 24 i - 16$ $9 -24i-16$	Combine like terms $63$ $63$ and $- 1$ $-1$ .
$=$ $=$	$- 7 - 24 i$ $-7-24i$

	$(6-6i)(7-6i)$	Multiply using the FOIL method.
$=$	$42 color(red)(-36i) color(red)(-42i)+36i^2$	Combine like terms $-36i$ and $-42i$ .
$=$	$42 color(red)(-78i)+36i^2$	Replace $i^2=-1$ .
$=$	$42-78i-36$	Combine like terms $63$ and $-1$ .
$=$	$6-78i$

	$(-4-5i)^2$	Expand $(-4-5i)^2$ .
	$(-4-5i)(-4-5i)$	Multiply using the FOIL method.
$=$	$16+color(red)(20i)+color(red)(20i)+25i^2$	Combine like terms $20i$ and $20i$ .
$=$	$16+color(red)(40i)+25i^2$	Replace $i^2=-1$ .
$=$	$16+40i-25$	Combine like terms $16$ and $-25$ .
$=$	$-9+40i$

	$(-2-3i)(-5+8i)$	Multiply using the FOIL method.
$=$	$10 color(red)(-16i)+color(red)(15i)-24i^2$	Combine like terms $-16i$ and $15i$ .
$=$	$10 color(red)(-i)-24i^2$	Replace $i^2=-1$ .
$=$	$10-i+24$	Combine like terms $10$ and $24$ .
$=$	$34-i$

Multiply Complex Numbers 2

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