Question

Express in the form of x+iy ,5+root2 i/2i

Answer 1

Step-by-step explanation:

5+√2i/2i=5+2i/2i×-2i/-2i

=-10i-4i²/4

=10i+4/4

=4/4+i10/4

= 1+i5/2

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 callled 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.