Question

Express (1+7i) in Eulerian form ​

Answer 1

Answer:

( 1 + 7i ) = (√50)е^(i81.87)

Step-by-step explanation:

We are given

1 + 7i

Comparing the 1 + 7i with x + yi we get

x = 1    and   y = 7

We know that

r² = x² + y²

Putting values we get

r² = 1² + 7² = 1 + 49 = 50

r² = 50

This implies

r = √50

And we know that

tan(α) = y / x = 7 / 1 = 7

tan(α) = 7

⇒ α = 81.87

We know that

x + yi = r( cos(α) + isin(α) )

So

( 1 + 7i ) = √50( cos(81.87) + isin(81.87) )

And we also know that

rе^(iα) = r( cos(α) + isin(α) )

So

( 1 + 7i ) = (√50)е^(i81.87)

Hence

( 1 + 7i ) = (√50)е^(i81.87)