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McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

2. Complex Numbers

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Exercise 40 Page 182

Recall that sqrt(- a)= isqrt(a).

x = ± 3i sqrt(2)

Practice makes perfect

To solve the given equation, let's first isolate x^2.

6x^2+108=0

LHS-108=RHS-108

6x^2=- 108

.LHS /6.=.RHS /6.

x^2=- 18

We cannot find any real square roots of a negative number, so we will need to use the fact that sqrt(- a)= isqrt(a) to solve for x.

x^2=- 18

sqrt(LHS)=sqrt(RHS)

x=± sqrt(- 18)

sqrt(- a)= isqrt(a)

x=± i sqrt(18)

SplitIntoFactors

Split into factors

x=± i sqrt(9 * 2)

sqrt(a* b)=sqrt(a)*sqrt(b)

x=± i sqrt(9) * sqrt(2)

Calculate root

x=± i * 3 * sqrt(2)

Multiply

x=± 3i sqrt(2)

Subchapter links

Exercises p.182-184