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maria [59]
2 years ago
5

Calculate 6+9i/-1+4i

Mathematics
1 answer:
lisabon 2012 [21]2 years ago
8 0

Multiply the numerator and denominator by the conjugate of the denominator:

\dfrac{6+9i}{-1+4i} \times \dfrac{-1-4i}{-1-4i} = \dfrac{(6+9i)(-1-4i)}{(-1)^2-(4i)^2}

Simplify:

\dfrac{(6+9i)(-1-4i)}{(-1)^2-(4i)^2} = \dfrac{-6-9i-24i-36i^2}{1-16i^2} = \dfrac{-6-33i-36i^2}{1-16i^2} = \dfrac{-6-33i+36}{1+16} = \boxed{\dfrac{30-33i}{17}}

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