if 2-3i =(4+i)(a+bi), then find the value of a and b.

2-3i=(4+i)(a+bi) then what is the value of a and b
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Expand brackets: 4a+4ib+ia-b=2-3i; (4a-b)+i(4b+a)=2-3i; 4a-b=2; 4b+a=-3 (equating real and imaginary components).

So substituting b=4a-2: 4(4a-2)+a=-3; 16a-8+a=-3; 17a=5, a=5/17, and b=4*5/17-2=-14/17.

by Top Rated User (1.1m points)

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