Question

Rationalize the denominator of:


`( √( - 49) )/((7 - 2i) - (4 - 9i))`
A.

`( - 49 + 2i)/( - 40)`
B.

`(49 + 21i)/(58)`
C.

`(77 + 21i)/( - 2)`
D.

`( - 77 + 21i)/(130)`

Answer 1

`\bf \cfrac{√(-49)}{(7-2i)-(4-9i)}\implies \cfrac{√(-1\cdot 49)}{(7-2i)-4+9i}\implies \cfrac{√(-1)\cdot √(49)}{3+7i} \\\\\\ \stackrel{\textit{multiplying top/bottom by the conjugate of the denominator }(3-7i)}{\cfrac{7i}{3+7i}\cdot \cfrac{3-7i}{3-7i}\implies \cfrac{7i(3-7i)}{\stackrel{\textit{difference of squares}}{(3+7i)(3-7i)}}\implies \cfrac{21i-(7i)^2}{[3^2-(7i)^2]}}`

`\bf \cfrac{21i-(7^2i^2)}{[9-(7^2i^2)]}\implies \cfrac{21i-(49(-1))}{[9-(49(-1))]}\implies \cfrac{21i+49}{9+49}\implies \cfrac{49+21i}{58}`