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mina [271]
2 years ago
9

Express each of the following complex numbers in the form of x+iy 1+i/3+i

Mathematics
1 answer:
grigory [225]2 years ago
3 0

I assume you mean the number

(1 + i) / (3 + i)

Multiply the numerator and denominator by the complex conjugate of 3 + i, which is 3 - i :

(1 + i) / (3 + i) • (3 - i) / (3 - i)

Recall the difference of squares identity,

a² - b² = (a + b) (a - b)

which makes the denominator of the product simplify to

(3 + i) (3 - i) = 3² - i² = 9 + 1 = 10

and so

(1 + i) / (3 + i) = (1 + i) (3 - i) / 10

Expand the numerator:

(1 + i) (3 - i) = 3 + 2i - i² = 4 + 2i

Then

(1 + i) / (3 + i) = (4 + 2i) / 10 = 2/5 + i 1/5

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4 0
2 years ago
4 1/2 divided by 2 3/8
Yuki888 [10]
First you make them mixed numbers:
9/2 ÷ 19/8
Then you flip the second fraction around
9/2 ÷ 8/19
Then you change ÷ to ×
9/2 × 8/19
And then multiply across!
72/38 = 1 34/38 = 1 17/19 (the final answer)
Hope this helps!
3 0
3 years ago
Please help me I would really appreciate it.
Karo-lina-s [1.5K]

Given:

\overline{AB}\cong \overline {CD},\overline{BC}\cong \overline {DA}

To prove:

\Delta CDA\cong \Delta ABC

Proof:

In \Delta CDA\text{ and } \Delta ABC,

\overline{AB}\cong \overline {CD} because Given

\overline{BC}\cong \overline {DA} because Given

\overline{AC}\cong \overline {AC} because Reflexive property.

Corresponding sides of both triangles are congruent. So,

\Delta CDA\cong \Delta ABC because SSS

Therefore, the required missing values are: Given, \overline{BC}\cong \overline {DA}, Reflexive property ,\Delta CDA\cong \Delta ABC, SSS respectively.

5 0
2 years ago
54 ÷ (−6)<br><br><br> A. 9<br><br> B. -9<br><br> C. -8
sp2606 [1]

Answer:

Option B, -9

Hope this helps!

6 0
2 years ago
Which statement is NOT true about Rational Numbers? *
serg [7]

Answer:

Integers, Whole Numbers, and Natural Numbers are Rational Numbers

Step-by-step explanation:

Hope it helps :3

3 0
2 years ago
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