All categories

2 years ago

What is the modulus of |9+40i|?

Mathematics

2 answers:

Gekata [30.6K]2 years ago

8 0

Answer: Modulus of |9+40i| =41

Step-by-step explanation:

Since we have given that

$z=\mid9+40i\mid$

Here,

$z=a+bi\\\\where,\\\\a=\text{real number}=9\\\\b=\text{imaginary number}=40$

We need to find the modulus of z:

$\mid z\mid=\sqrt{a^2+b^2}$

$\mid z\mid=\sqrt{9^2+40^2}\\\\\mid z\mid=\sqrt{81+1600}\\\\\mid z\mid=\sqrt{1681}\\\\\mid z\mid=41$

Hence, Modulus of |9+40i| =41

Talja [164]2 years ago

6 0

Answer:

Step-by-step explanation:

We know that complex numbers are a combination of real and imaginary numbers

Real part is x and imaginary part y is multiplied by i, square root of -1

Modulus of x+iy = $\sqrt{x^2+y^2}$

Here instead of x and y are given 9 and 40

i.e. 9+40i

Hence to find modulus we square the coefficients add them and then find square root

|9+49i| = $\sqrt{9^2+40^2} =\sqrt{1681}$

By long division method we find that

|9+40i| =41

You might be interested in

What is the probability that a fair die never comes up an even number when it is rolled six times? (note: enter the value of pro

seropon [69]

Let us compute first the probability of ending up an odd number when rolling a dice. A dice has faces with numbers 1 up to 6. The odd numbers within that is 3 (1, 3 and 5). Therefore, each dice has a probability of 3/6 or 1/2. Then, you use the repeated trials formula:

Probability = n!/r!(n-r)! * p^r * q^(n-r), where n is the number of tries (n=6), r is the number tries where you get an even number (r=0), p is the probability of having an even face and q is the probability of having an odd face.

Probability = 6!/0!(6!) * (1/2)^0 * (1/2)^6
Probability = 1/64

Therefore, the probability is 1/64 or 1.56%.

6 0

3 years ago

<img src="https://tex.z-dn.net/?f=%5Cfrac%7B3%2F7%7D%7B7%5Csqrt%7B10%7D%2F2%20%7D" id="TexFormula1" title="\frac{3/7}{7\sqrt{10}

VashaNatasha [74]

Multiply the numerator and denominator by 7×2 = 14 to eliminate the denominators of those fractions:

$\dfrac{\dfrac37}{\dfrac{7\sqrt{10}}2}\times\dfrac{14}{14}=\dfrac{3\times2}{7\sqrt{10}\times7}=\dfrac6{49\sqrt{10}}$

Rationalize the denominator by multiplying both numerator and denominator by √10:

$\dfrac6{49\sqrt{10}}\times\dfrac{\sqrt{10}}{\sqrt{10}}=\dfrac{6\sqrt{10}}{49(\sqrt{10})^2}=\dfrac{6\sqrt{10}}{49\times10}=\dfrac{6\sqrt{10}}{490}$

Lastly, cancel the common factor of 2 in both the numerator and denominator (which comes from 6 = 2×3 and 490 = 2×245):

$\dfrac{6\sqrt{10}}{490}=\dfrac{3\sqrt{10}}{245}}$

8 0

2 years ago

Tina's favorite shade of teal is made with 7 ounces of blue paint for every 5 ounces of green paint. Tyler's favorite shade of t

Eddi Din [679]

Answer:

<em>A. Tina's favorite shade is more blue than Tyler's</em>

6 0

3 years ago

Read 2 more answers

Suppose m∠YES = 113°

s344n2d4d5 [400]

By definition, complementary angles add up to 90°

Let
$x$
be the complement of 113°

Then,

$x + 113 \degree = 90 \degree$

$x = 90 - 113 = - 23 \degree$

By definition supplementary angles also add up to 180°

Let
$y$
be the supplement of 113°

Then,

$y + 113 = 180$
$y = 180 - 113 = 67 \degree$
Hence the supplement of m<YES=67°

6 0

3 years ago

Simplify the expression 2x^2 + 5x - 3 - 5x^2 + 7 - 3x

Ira Lisetskai [31]

Answer:-3x^2+2x+4

Step-by-step explanation: hope i helped

6 0

2 years ago

Read 2 more answers