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Math Asked by a SnapAndSolve user · about 2 hours ago

Write the following numbers in a + bi form: (a) (-5 - 2i)(5 - i)(5 + i) = _ + _ i. (b) ((-1 + 3i)^2 -...

Write the following numbers in a + bi form:
(a) (-5 - 2i)(5 - i)(5 + i) = ___ + ___ i.
(b) ((-1 + 3i)^2 - 2)i = ___ + ___ i.

Answer

First, simplify (-5 - 2i)(5 - i)(5 + i):

Calculate (5 - i)(5 + i) = 25 - i^2 = 25 + 1 = 26.

Now, multiply (-5 - 2i) by 26:

(-5 - 2i) * 26 = -130 - 52i.

So, the answer is -130 + (-52)i.
First, simplify ((-1 + 3i)^2 - 2)i:

Calculate (-1 + 3i)^2 = (-1)^2 + 2(-1)(3i) + (3i)^2 = 1 - 6i - 9 = -8 - 6i.

Subtract 2: (-8 - 6i) - 2 = -10 - 6i.

Multiply by i: (-10 - 6i)i = -10i - 6i^2 = -10i + 6 = 6 - 10i.

So, the answer is 6 + (-10)i.

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