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separate into real and imaginary parts and find the multiplicative inverse of √2+i/√2-i (only 2 is in the √

Sagot :

samuelonum1

The multiplicative inverse for √2-i = 1/(√2+1) and  The multiplicative inverse is √2+1 = 1/(√2-1)

Real and Imaginary Numbers/Complex Numbers

Given Data

  • First expression = √2+i
  • Second expression = √2-i

For√2+i

the real part is  is √2 and the imaginary part is i

The multiplicative inverse is √2+1 = 1/(√2-1)

rationalising the denominator we have

= 1/√2-1 * √2-1/√2-1

= √2-1/(√2-1)*(√2-1)

= √2-1/(2-√2-√2+1)

= √2-1/(-2√2+3)

For√2-i

the real part is  is √2 and the imaginary part is -i

The multiplicative inverse is √2-1 = 1/(√2+1)

Rationalising the denominator we have

= 1/√2+1 * √2+1/√2+1

= √2+1/(√2+1)*(√2+1)

= √2+1/(2+√2+√2+1)

= √2+1/(2√2+3)

Learn more about complex Numbers here

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