Complex numbers/find a and b

**Adam We** · February 21st 2009, 01:51 AM

Find real numbers a and b such that

(a+bi)(1+bi) = 17-19i

Thank you very much,
Adam

**james_bond** · February 21st 2009, 03:55 AM

$(a+bi)(1+bi) =a-b^2+(ab+b)i= 17-19i$ So $a-b^2=17$ and $ab+b=-19$ . You can solve for $a$ and $b$ . I've got only one real solution: $a=18$ , $b=-1$ .

**Plato** · February 21st 2009, 03:59 AM

$\left( {a + bi} \right)\left( {1 + bi} \right) = \left( {a - b^2 } \right) + \left( {ab + b} \right)i$

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