What is ((6+3j)^2)/((2-4j)+8)<30 ?

The solution to ((6+3j)^2)/((2-4j)+8) 5/2

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((6+3j)^2)/((2-4j)+8)<30

\frac{( 6 + 3 j ) ^{2}}{( 2 - 4 j ) + 8} < 30

- \frac{2 ( 13 + 235 )}{3} < j < \frac{2 ( 235 - 13 )}{3} or j > \frac{5}{2}

Interval Notation

(- \frac{2 ( 13 + 235 )}{3}, \frac{2 ( 235 - 13 )}{3}) \cup (\frac{5}{2}, \infty)

Decimal Notation

- 18.88647 \dots < j < 1.55313 \dots or j > 2.5

Solution steps

\frac{( 6 + 3 j ) ^{2}}{2 - 4 j + 8} < 30

Rewrite in standard form

\frac{9 j ^{2} + 156 j - 264}{- 4 j + 10} < 0

Factor

\frac{9 j ^{2} + 156 j - 264}{- 4 j + 10} : \frac{3 ( 3 j ^{2} + 52 j - 88 )}{- 2 ( 2 j - 5 )}

\frac{3 ( 3 j ^{2} + 52 j - 88 )}{- 2 ( 2 j - 5 )} < 0

Simplify

\frac{3 ( 3 j ^{2} + 52 j - 88 )}{- 2 ( 2 j - 5 )} < 0

Multiply both sides by

- 1

(reverse the inequality)

\frac{3 ( 3 j ^{2} + 52 j - 88 ) ( - 1 )}{- 2 ( 2 j - 5 )} > 0 \cdot (- 1)

Simplify

\frac{3 ( 3 j ^{2} + 52 j - 88 )}{2 ( 2 j - 5 )} > 0

Multiply both sides by

2

\frac{2 \cdot 3 ( 3 j ^{2} + 52 j - 88 )}{2 ( 2 j - 5 )} > 0 \cdot 2

Simplify

\frac{3 ( 3 j ^{2} + 52 j - 88 )}{2 j - 5} > 0

Divide both sides by

3

\frac{\frac{3 ( 3 j ^{2} + 52 j - 88 )}{2 j - 5}}{3} > \frac{0}{3}

Simplify

\frac{3 j ^{2} + 52 j - 88}{2 j - 5} > 0

Identify the intervals

- \frac{2 ( 13 + 235 )}{3} < j < \frac{2 ( 235 - 13 )}{3} or j > \frac{5}{2}

\frac{( 3 x ^{2} )}{( x ^{2} - 1 )} < 0

(x^{2} + 8) (x - 4) (x + 2) < 0

\frac{3}{( 1 - x )} \leq 2

6 x^{3} - 9 x^{2} + 3 < 0

\frac{( x ^{2} + x + 1 )}{x} > 3

What is ((6+3j)^2)/((2-4j)+8)<30 ?
The solution to ((6+3j)^2)/((2-4j)+8)<30 is -(2(13+sqrt(235)))/3 <j<(2(sqrt(235)-13))/3 \lor j> 5/2