Question

(x+iy)^5 i need this in U +iv form​

Answer 1

Step-by-step explanation:

if i is in form of ( x+iy)ⁿ×i

(x+iy)^5i. = i ( x+iy) ( x+iy) ⁴

- ( y-ix) [ ( x+iy)²]²

- ( y-ix) [ x²-y²+2ixy]²

-(y-ix) [ (x²-y²)²-4x²y²+ 4ixy]

[-y( x²-y²)²+4x²y³-4ixy²+ix( x²-y²)²-4ix³y²-4x²y]

[ {-y( x²-y²)²+4x²y³- 4x²y}. =>>>>>>>>Real - { 4xy²-x( x²-y²)²+4x³y²} i ]=>>>>>>>>imaginary

= X+ iY

where X= real part and Y is imaginary part

if i is in form of ( x+i y)ⁿi

( x+ i y) ^5i=[ (x+iy)^5]^i

[ { (x+iy)^5²}i²]½

[{( x+ iy)^5²}^-1]½

[{ x+iy}^(-25)]½

= (x+iy)^-25/2

this is form of (X+ iy)