37-What is the reciprocal of the conjugate of 2√5 - 3√2 ? 38- show that the reciprocal of ((√5 + 1 ) / 2 ) is also the conjugate of ((√5 + 1 ) / 2 )?

conjugate
reciprocal

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37-What is the reciprocal of the conjugate of 2√5 - 3√2 ??
38- show that the reciprocal of ((√5 + 1 ) / 2 ) is also the conjugate of ((√5 + 1 ) / 2 ) ?

Answer:

The conjugate of a complex number is the number itself, with the sign of the imaginary part changed:
Example:
Complex number (a + bi), conjugated → (a – bi)
The reciprocal or multiplicative inverse of a complex number is the reciprocal of the given multiplied, top and bottom, by the conjugate of the number
Example:
Complex number (a + bi), reciprocal → 1/(a + bi), for the reciprocal operation of complex number → [1/(a + bi)]. [(a - bi)/(a - bi)]
37.The conjugate of (2√5 - 3√2i) is → (2√5 + 3√2i)
The reciprocal of (2√5 + 3√2i) is → [1/(2√5 + 3√2i)]. [(2√5 - 3√2i) / (2√5 - 3√2i)]
Solving and simplifying we have for the reciprocal
(2√5 - 3√2i)/(20 - 18) = (2√5 - 3√2i)/2
38. The conjugate of (√5 + 1i)/2 is → (√5 - 1i)/2
The reciprocal of (√5 + 1i)/2 is: → [2/(√5 + 1i)]. [(√5 - 1i)/(√5 - 1i)]
Solving and simplifying we have for the reciprocal
(2√5 - 2i)/4 = (√5 - 1i)/2, which is equal to the conjugate