Simplify (1+2i)(5-3i)

Mathematics

1 answer:

Vesna [10]3 years ago

8 0

Answer: 11+7i

Step-by-step explanation: Multiply using the PIL mthod, then combine the real imaginary parts of the expression.

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Genrish500 [490]

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4 years ago

G find the domain for the particular solution to the differential equation dy dx equals the quotient of negative 1 times x and y

faust18 [17]

$\frac{dy}{dx} = \frac{-x}{y}$
by separating the variables
∴ y dy = -x dx
integrating both sides with respect to x
∴ ∫y dy = ∫-x dx
∴ $\frac{ y^{2} }{2} = - \frac{ x^{2} }{2} +c$
finding c using initial condition y(2) = 2.
∴ $\frac{ 2^{2} }{2} = - \frac{ 2^{2} }{2} +c$
∴ c = 4
∴ $\frac{ y^{2} }{2} = - \frac{ x^{2} }{2} +4$
multiplying all the equation by 2
∴ y² = -x² + 8
∴ x² + y² = 8
The resultant equation represents the equation of the circle
with center (0,0) and radius = √8 = 2√2
so, the domain of this function is [-2√2 , 2√2]
See the attached figure