Question

Express 5+i root 2 / 2i in the form of x+iy

Answer 1

Step-by-step explanation:

Given Express 5+i root 2 / 2i in the form of x+iy

• Given 5 + I √2 / 2i
• Now rationalising the denominator we get
• 5 + I √2 / 2i x 2i / 2i
• = 10i + 2 √2i^2 / 4 i^2
• = 10 i - 2 √2 / - 4
• = √2 / 2 – 5i / 2

Reference link will be

https://brainly.in/question/12436278

Answer 2

$1-\dfrac{5}{\sqrt{2}}i$ in the form of x + iy.

Step-by-step explanation:

We have,

$\dfrac{5+\sqrt{2}i}{2i}$

To express in the form of x + iy = ?

∴ $\dfrac{5+\sqrt{2}i}{2i}$

Multiplying numerator and denominator by i, we get

=$\dfrac{(5+\sqrt{2}i)\times i}{2i\times i}$

$=\dfrac{5i+\sqrt{2}i^2}{2i^2}$

We know that,

In complex number,

$i^{2}$ = - 1, i is called imaginary part of z.

= $\dfrac{5i-\sqrt{2}}{-2}$

= $\dfrac{-\sqrt{2}+5i}{-2}$

Separating real and imaginary part, we get

$=\dfrac{-\sqrt{2}}{-\sqrt{2}}+\dfrac{5}{-\sqrt{2}}i$

= $1-\dfrac{5}{\sqrt{2}}i$

1 is the real part of the complex number and

$-\dfrac{5}{\sqrt{2}}$ is the imaginary part of complex number

Thus, $1-\dfrac{5}{\sqrt{2}}i$ in the form of x + iy.