Write the expression as a complex number in standard form 7

Write the expression as a complex number in standard form. 7 - i/2 + 7i

given (7 - i)/(2+7i)

congugate of (2+7i) is (2 -7i)

now mutiply and divide the given expression with (2 - 7i)

(7-i)(2-7i)/(2+7i)(2-7i)

= [7*2 -7*7i -2i +7i^2] / [2^2 - (7i)^2 ]

= [ 14 -49i -2i -7 ] / [ 4 -49i^2] { since i^2 =-1}

= [ 7 -51i]/(4+49) { since i^2=-1}

=[7 - 5i]/53

= 7/53 - 5i/53

this is of the form a+bi is complex number