Express (15 - 20i)/(1-2i) in a+bi form.
Thank you for all of the help!
since (a-bi)(a+bi) = a^2+b^2, we have
(15-20i)(1+2i)
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(1-2i)(1+2i)
= (15-20i+30i-40i^2)/(1^2+2^2)
= (55+10i)/5
= 11+2i
Thank you so much for your help Steve!
To express the complex number (15 - 20i)/(1 - 2i) in the form a + bi, where a and b are real numbers, you need to rationalize the denominator. Rationalizing the denominator involves multiplying both the numerator and denominator by the conjugate of the denominator.
The conjugate of 1 - 2i is 1 + 2i, which means we multiply both numerator and denominator by 1 + 2i:
((15 - 20i)/(1 - 2i)) * ((1 + 2i)/(1 + 2i)) =
((15 - 20i)*(1 + 2i))/(1 - 4i^2) =
(15 + 30i - 20i - 40i^2)/(1 + 4) =
(15 + 10i - 40(-1))/(5) =
(15 + 10i + 40)/(5) =
(55 + 10i)/(5) =
11 + 2i
Therefore, (15 - 20i)/(1 - 2i) can be expressed in the form a + bi as 11 + 2i.