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4 years ago

How can I factor these complex conjuages? a^2 + b^2 and a^2 - b

Mathematics

2 answers:

erica [24]4 years ago

8 0

Answer:

1) $(a+ib)(a-ib)$

2) $a^2+i^2b$

Step-by-step explanation:

1) $a^2+b^2$

=> $a^2 - (-1)b^2$ (We know that -1 = $i^2$ )

=> $a^2-i^2b^2$

=> $(a)^2-(ib)^2$

Using Formula $a^2 -b^2 = (a+b)(a-b)$

=> $(a+ib)(a-ib)$

2) $a^2-b$

=> $a^2+(-1)b$ (We know that -1 = $i^2$ )

=> $a^2+i^2b$ (It cannot be simplified further)

Marat540 [252]4 years ago

6 0

Answer:

$\boxed{(a+ib)(a-ib)}$

$\boxed{a^2+i^2b}$

Step-by-step explanation:

$a^2 + b^2$

Rewrite expression.

$a^2- (-1)b^2$

Use identity : $-1=i^2$

$a^2- i^2 b^2$

Factor out square.

$a^2-(ib)^2$

Apply difference of two squares formula : $a^2-b^2 =(a+b)(a-b)$

$(a+ib)(a-ib)$

$a^2-b$

Rewrite expression.

$a^2+(-1)b$

Use identity : $-1=i^2$

$a^2+i^2b$

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