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3 years ago

(3+i)^2 = c+di, find the value of d.

Mathematics

1 answer:

inna [77]3 years ago

3 0

Answer:

d. $\displaystyle 6$

Step-by-step explanation:

$\displaystyle [3 + i]^2 = [3 + i][3 + i] = 9 + 6i + i^2 → 9 + 6i - 1 → 6i + 8$

Therefore, the d-value is 6.

Extended Information on the Complex Number System

$\displaystyle \sqrt{-1} = i \\ -1 = i^2 \\ -i = i^3 \\ 1 = i^4\:[every\:multiple\:of\:4]$

I am joyous to assist you anytime.

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The number 6 is halfway between 4.5 and 7.5.

Natasha2012 [34]

$6=\frac{2.8+x}{2}\\
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3 years ago

Find the distance to the nearest tenth,between S(6,5) and T(-3,-4)

Doss [256]

Answer:

<h3>The answer is 12.7 units</h3>

Step-by-step explanation:

The distance between two points can be found by using the formula

$d = \sqrt{ ({x1 - x2})^{2} + ({y1 - y2})^{2} } \\$

where

(x1 , y1) and (x2 , y2) are the points

From the question the points are

S(6,5) and T(-3,-4)

The distance between them is

$|ST| = \sqrt{ ({6 + 3})^{2} + ({5 + 4})^{2} } \\ = \sqrt{ {9}^{2} + {9}^{2} } \\ = \sqrt{81 + 81} \\ = \sqrt{162} \\ = 9 \sqrt{2} \: \: \\ = 12.7279...$

We have the final answer as

<h3>12.7 units to the nearest tenth</h3>

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