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Citrus2011 [14]
3 years ago
13

What is the midpoint between -2-3i and 3+9i

Mathematics
1 answer:
Svetlanka [38]3 years ago
3 0

Answer:

1/2 + 3i is the midpoint between -2-3i and 3+9i.

Step-by-step explanation:

Given the complex number

  • -2-3i
  • 3+9i

The formula to find the midpoint of two complex number (a + bi) and (c + di) is:

M=\frac{\left(a+c\right)}{2}+\frac{\left(b+d\right)i}{2}

M=\frac{\left(-2+3\right)}{2}+\frac{\left(-3+\left(9\right)\right)i}{2}

M=\frac{-2+3+\left(-3+9\right)i}{2}

M=\frac{1+6i}{2}

M=\frac{1}{2}+3i

Therefore, 1/2 + 3i is the midpoint between -2-3i and 3+9i.

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<h3>Answer: D) 3/150</h3>

==========================================================

Explanation:

With the use of a calculator, we see that,

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The word "terminate" means "stop". In the other decimal values, the decimal digits go on forever repeating the patterns mentioned.

----------------------

A non-calculator approach will have us simplify 3/150 into 1/50 after dividing both parts by the GCF 3. Then notice how 50 has the prime factorization of 2*5*5. The fact that the denominator 50 can be factored in terms of only 2's and 5's is enough evidence to conclude that the fraction converts to a terminating decimal.

If the denominator factors into some other primes, other than 2s and 5s, then we don't have a terminating decimal. So that's why 11/19, 4/7 and 1/3 convert to non-terminating decimals.

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