In a+bi form, the reciprocal of 2+6i is

Options

A. `1/2+1/6i`
B. `-1/(16)+3/(16_i`
C. `1/(16)+3/(16)i`
D. `1/(20)-3/(20)i`

Answer

D

Explanation

Enter `(1)/(2+6i)`j into your calculator and press MATH/ENTER/ENTER/ to get FRACTIONAL real and imaginary parts. An alternative solution is to multiply the numerator and denominator of `(1)/(2+6i)` by the complex conjugate 2-6i:
`(1)/(2+6i)*(2-6i)/(2-6i)=(2-6i)/(4-(-36))=1/(20)-3/(20)i` [17]