Question

√2(cos7π|4+isin7π|4)​

Answer 1

Answer:

$\sqrt{2}(e^{i\frac{7\pi}{4}})$

Step-by-step explanation:

In the question,

We have been given,

$\sqrt{2}(cos(\frac{7\pi}{4}) +isin(\frac{7\pi}{4}))$

Now, we can say that,

$cos\theta+isin\theta$ can be written as $e^{i\theta}$.

So,

We can write it as,

$\sqrt{2}(e^{i\frac{7\pi}{4}})$

Now also, we know that in the equation of the form,

$re^{i\theta}$

'r' is the magnitude.

and,

θ is the angle.

So, we can write it as $\sqrt{2}(e^{i\frac{7\pi}{4}})$

Here, $\sqrt{2}$ is the magnitude of the vector given and $\frac{7\pi}{4}$ is the angle made by the vector with the x-axis.