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3 years ago

Find the numerical value of each expression. (Round your answers to five decimal places.) (a) sinh(0) (b) cosh(0)

Mathematics

1 answer:

Ahat [919]3 years ago

8 0

Hehnehdsudbdbsvshndbx

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Suppose a and b are both non zero real numbers. Find real numbers c and d such that 1/a+ib= c+id

Thepotemich [5.8K]

$\begin{gathered} c=\frac{a}{a^2+b^2} \\ d=\frac{-b}{a^2+b^2} \end{gathered}$

Explanation

$\frac{1}{a+bi}=c+di$

Step 1

multiplicate by the conjugate

$\begin{gathered} \frac{1}{a+bi}\cdot\frac{a-bi}{a+bi}=\frac{a-bi}{(a+bi)(a-bi)}=\frac{a-bi}{a^2-(bi)^2} \\ \frac{1}{a+bi}\cdot\frac{a-bi}{a+bi}=\frac{a-bi}{(a+bi)(a-bi)}=\frac{a-bi}{a^2-(-b^2)}=\frac{a-bi}{a^2+b^2} \end{gathered}$

notice that

$\begin{gathered} \frac{1}{a+bi}=\frac{a-bi}{a^2+b^2}=\frac{a}{a^2+b^2}-\frac{b}{a^2+b^2}i \\ \frac{a}{a^2+b^2}-\frac{b}{a^2+b^2}i=c+di \\ so \\ \end{gathered}$ $\begin{gathered} c=\frac{a}{a^2+b^2} \\ d=\frac{-b}{a^2+b^2} \end{gathered}$

I hope this helsp you

6 0

1 year ago

Select the fraction that is equal to 2/4<br> 1/5<br> 12/7<br> 1/2

polet [3.4K]

Answer:

1/2

hope this helps

have a good day :)

Step-by-step explanation:

6 0

2 years ago

Evaluate [-1 -(-3) ] × (-4)

7nadin3 [17]

Answer:

the answer is -8.

Step-by-step explanation:

hope this helps!

8 0

2 years ago

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What is 692,004 in expanded form

rjkz [21]

600000+90000+2000+4=692004

I think that's how you write it.

5 0

3 years ago

Read 2 more answers

What is the distance between the points (-1,4) and (7,4)?

user100 [1]

Answer:

Step-by-step explanation:

=(7−(−1))2+(4−4)2‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾√

=(8)2+(0)2‾‾‾‾‾‾‾‾‾‾√

=64+0‾‾‾‾‾‾√

=6‾√4

8 0

3 years ago