Question

1/a+ib=3-2i find a and b​

Answer 1

Answer:

a = 3/13 and b = 2/13

Step-by-step explanation:

Given

$\frac{1}{a+ib} =3-2i$

$\implies\frac{1}{3-2i} =a+ib$

$\implies a+ib=\frac{1}{3-2i} \times\frac{3+2i}{3+2i}$   (Multiplying the numerator and denominator with the conjugate of 3-2i i.e. 3+2i)

$\implies a+ib=\frac{3+2i}{(3-2i)(3+2i)}$

$\implies a+ib=\frac{3+2i}{3^2-(-2i)^2}$

$\implies a+ib=\frac{3+2i}{9-4i^2}$

$\implies a+ib=\frac{3+2i}{9+4}$      (∵ i^2 = -1)

$\implies a+ib=\frac{3+2i}{13}$

$\implies a+ib=\frac{3}{13}+\frac{2}{13} i$

Comparing real and imaginary parts we get

a = 3/13 and b = 2/13

Answer 2

Answer:

a=3/13 and b=2/13

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