Question

5+4i/4+5i express in a+ib

Answer 1

HEYA!!
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$\frac{5 + 4i}{4 + 5i} \times \frac{4 - 5i}{4 - 5i} \\ \\ \\ = \frac{5(4 - 5i) + 4i(4 - 5i)}{(4) {}^{2} - (5i) {}^{2} } \\ \\ = \frac{20 - 25i + 16i - 20i {}^{2} }{16 - 25i {}^{2} } \\ \\ = \frac{20 - 9i + 20}{16 + 25} \\ \\ = \frac{40 - 9i}{41} \\ \\ = \frac{40}{41} - \frac{9i}{41}$
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Answer 2

MULTIPLY BY (4-5i)/(4-5i)

then denominator = (4)^2 + (5i)^2 = 16 - 25i^2 = 16 + 25 = 41

Numerator = 20 -25i +16i -20i^2 = 20 -9i +20 = 40-9i

so (40-9i)/(41) = (-40/41 + 9/41 i)