Question

Use Euler's formula to write 5√√2-51-√√2 in exponential form.
O 10e
10.¹

Answer 1

To write 5√√2-51-√√2 in exponential form, we can use Euler's formula. By applying the formula and simplifying the given expression, we arrive at the exponential form e^(5/2 * i * (√√2)) - e^(1/2 * i * (√√2)) - 51.

Step-by-step explanation:

Euler's formula states that for any real number x:

e^(ix) = cos(x) + i * sin(x)

We can use this formula to write 5√√2-51-√√2 in exponential form.

5√√2-51-√√2 can be simplified to 5√√2 - √√2 - 51 = 5√√2 - 1(√√2) - 51 = (√√2)^(5/2) - (√√2)^(1/2) - 51

Now we can rewrite (√√2)^(5/2) and (√√2)^(1/2) using Euler's formula:

(√√2)^(5/2) = e^(5/2 * i * (√√2))

(√√2)^(1/2) = e^(1/2 * i * (√√2))

Substituting these values back into the original equation:

5√√2 - √√2 - 51 = e^(5/2 * i * (√√2)) - e^(1/2 * i * (√√2)) - 51

So, 5√√2-51-√√2 in exponential form is e^(5/2 * i * (√√2)) - e^(1/2 * i * (√√2)) - 51.

Learn more about Writing expressions in exponential form