Question

Show all work to multiply (6+square root -64)(3-square root -16)

Answer 1

Answer:

50

Step-by-step explanation:

Given expression,

$(6+\sqrt{-64})\times (3-\sqrt{-16})$

$=(6+\sqrt{-(8^2)})\times (3-\sqrt{-(4^2)})$

$=(6+8\sqrt{-1})\times (3-4\sqrt{-1})$

$=(6+8i)(3-4i)$       ( ∵ √-1 = i )

$=6(3-4i)+8i(3-4i)$

$=18-24i+24i-32i^2$

$=18+32$    ( ∵ i² = -1 )

$=50$

Answer 2

Answer:

50

Step-by-step explanation:

- 8i = √-64

8i + 6

- -4i = -√-16

-4i + 3

[8i + 6][-4i + 3] → FOIL

>> -32i² + [24i - 24i] + 18

↑ ↑

-1 0

>>> 32 + 18 = 50

Information on Imaginary Numbers

√-1 = i

-1 = i²

-i = i³

1 = i⁴ [And every other exponent that is a multiple of 4; this cycle then repeats itself every time you go up one number at a time]

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