Question

1. - / 1 points

write the complex number in standard form.
$-2i^{2}+4i$
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1. - / 1 points

perform the operation and write the result in standard form.
$left(sqrt{2}+sqrt{15}i
ight)left(sqrt{2}-sqrt{15}i
ight)$
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1. - / 1 points

perform the operation and write the result in standard form.
$(2 - 5i)^{2}-(2 + 5i)^{2}$
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Explanation:

Step1: Substitute $i^2=-1$

$-2(-1) + 4i$

Step2: Simplify the real term

$2 + 4i$

Step1: Apply difference of squares

$(\sqrt{2})^2 - (\sqrt{15}i)^2$

Step2: Calculate each squared term

$2 - (15i^2)$

Step3: Substitute $i^2=-1$

$2 - 15(-1)$

Step4: Simplify the expression

$2 + 15 = 17$

Step1: Expand each squared binomial

$(4 - 20i + 25i^2) - (4 + 20i + 25i^2)$

Step2: Substitute $i^2=-1$

$(4 - 20i -25) - (4 + 20i -25)$

Step3: Simplify each parenthesis

$(-21 -20i) - (-21 + 20i)$

Step4: Distribute the negative sign

$-21 -20i +21 -20i$

Step5: Combine like terms

$-40i$

Answer:

1. $2 + 4i$
2. $17$
3. $-40i$