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How do you perform the operation and write the result in standard form given #(8+sqrt(-18))-(4+3sqrt2i)#?

Answer 1

Benjamin Achtenberg

#(8+sqrt(-18))-(4+3sqrt2 i)=4#

While dealing with complex numbers always remember #i^2=-1# and #sqrt(-1)=i#.

Hence, #(8+sqrt(-18))-(4+3sqrt2 i)#

= #(8+sqrt(3×3×2×(-1)))-(4+3sqrt2 i)#

= #8+3sqrt2 i-4-3sqrt2 i#

= #4#

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Answer 2

Sophie Adams

To perform the operation and write the result in standard form, you simplify each part separately and then combine like terms. Here's the simplified process:

Simplify (8 + \sqrt{-18}) to (8 + 3i\sqrt{2}).
Simplify (4 + 3\sqrt{2}i) to (4 + 3i\sqrt{2}).
Subtract the simplified expressions: ((8 + 3i\sqrt{2}) - (4 + 3i\sqrt{2})).
Combine like terms: (8 - 4 + (3i\sqrt{2} - 3i\sqrt{2})).
Perform the subtraction: (4 + 0i = 4).

So, the result in standard form is (4).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.