Question

If Z = $\frac{13-5i}{4-9i}$ can be written in a+ib. Find the value of a+b.

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Answer 1

z=$\frac{13-5i}{4-9i}$

Rationalize the given complex number by multiplying 4+9i in both numerator and denominator

= $\frac{13-5i}{4-9i}$ $\times$ $\frac{4+9i}{4+9i}$

= $\frac{52-20i+117i-42i^2}{16-81i^2}$

=$\frac{97+97i}{97}$

=1 + i

Compare with a+ib, a=1, b=1, a+b=2