Question

Use the conjugate to divide1 - i / square root of 3 + 4i

Answer 1

Explanation:

(1 - i) / (sqrt(3 + 4i)

= (1 - i) /
`√(3 + 4i)`

=> multiply and divide by conjugate of denominator

=
`(1 - i) / √(3 + 4i) * √(3 - 4i) / √(4 - 3i)`

=
`(1 - i)*(√(3 - 4i) ) / (√(3 + 4i) *√(3 - 4i))`

=
`(1 - i) * (√(3 - 4i) ) / \sqrt{(9 - 16i^(2) )`

=
`(1 - i) * (√(3 - 4i) ) / \sqrt{(9 - (-16) )`

=
`(1 - i) * √(3 - 4i) ) / √(25)`

=
`(1 - i) * √(3 - 4i) / 5`

=
`\sqrt{(1 - i)^(2) } * √(3 - 4i) / 5`

=
`√((1 + -1 -2i)*(3 - 4i)) / 5 \\√(-2i * (3 - 4i)) / 5\\√(-6i + 8*-1) /5 \\√(-6i - 8 ) / 5`