Question

Express (1+7i) in Eulerian form.​

Answer 1

Answer:

The expression is euler formula is given as √50 ( cos(81. 86) + i son (81.86).

Step-by-step explanation:

To solve:

Express (1+7i) in Eulerian form.​

According to Eulerian formula,

a+bi = rcos θ + r i sin θ

1+7i = r cos θ + r i sinθ

Thus rcos θ = 1

r sinθ = 7

r = √(1) ^2+ (7) ^

r = √ 1+49

r = √50

rcos θ = 1

Hence,

cos θ = 1/r

= 1/√50

Hence, θ = 81.86

Also,

r sinθ = 7

Hence,

sinθ = 7/r

sinθ = 7/√50

Hence, θ = 81.86

Euler form is expressed as

a+bi = rcos θ + r i sin θ

1+7i = r (cos θ + i sin θ)

= √50 ( cos(81. 86) + i son (81.86)

Hence, the expression is euler formula is given as √50 ( cos(81. 86) + i son (81.86)