Answer:
19
Step-by-step explanation:
15z-14z=12+7
z=19
Answer:
You are awesome :)
Step-by-step explanation:
Thank you!!
Given that triangle m and n are similar, then the implication is the ratio of the corresponding sides are the same and the corresponding angles are equal. This implies that if the two angles of triangle m measure 32° and 93°, then the possible size for the two angles in triangle n will be 32° and 93°.
Answer:
![2 \sqrt{2} + i \sqrt{2}](https://tex.z-dn.net/?f=2%20%5Csqrt%7B2%7D%20%20%2B%20i%20%5Csqrt%7B2%7D%20)
Step-by-step explanation:
The square of a complex number is a complex number. Here, we have:
![{(a + bi)}^{2} = 6 + 8i](https://tex.z-dn.net/?f=%20%7B%28a%20%2B%20bi%29%7D%5E%7B2%7D%20%20%3D%206%20%2B%208i)
![{a}^{2} + 2abi - {b}^{2} = 6 + 8i](https://tex.z-dn.net/?f=%20%7Ba%7D%5E%7B2%7D%20%20%2B%202abi%20-%20%20%7Bb%7D%5E%7B2%7D%20%20%3D%206%20%20%2B%208i)
We then have this system of equations:
![{a}^{2} - {b}^{2} = 6](https://tex.z-dn.net/?f=%20%7Ba%7D%5E%7B2%7D%20%20-%20%20%7Bb%7D%5E%7B2%7D%20%20%3D%206)
![2ab = 8](https://tex.z-dn.net/?f=2ab%20%3D%208)
Solving this system:
![ab = 4](https://tex.z-dn.net/?f=ab%20%3D%204)
![b = \frac{4}{a}](https://tex.z-dn.net/?f=b%20%3D%20%20%5Cfrac%7B4%7D%7Ba%7D%20)
![{a}^{2} - {( \frac{4}{a}) }^{2} = 6](https://tex.z-dn.net/?f=%20%7Ba%7D%5E%7B2%7D%20%20-%20%20%7B%28%20%5Cfrac%7B4%7D%7Ba%7D%29%20%7D%5E%7B2%7D%20%3D%206%20)
![{a}^{2} - \frac{16}{ {a}^{2} } = 6](https://tex.z-dn.net/?f=%20%7Ba%7D%5E%7B2%7D%20%20-%20%20%5Cfrac%7B16%7D%7B%20%7Ba%7D%5E%7B2%7D%20%7D%20%3D%206%20)
![{a}^{4} - 16 = 6{a}^{2}](https://tex.z-dn.net/?f=%20%20%7Ba%7D%5E%7B4%7D%20%20-%2016%20%3D%20%206%7Ba%7D%5E%7B2%7D%20)
![{a}^{4} - 6 {a}^{2} - 16 = 0](https://tex.z-dn.net/?f=%20%7Ba%7D%5E%7B4%7D%20%20-%206%20%7Ba%7D%5E%7B2%7D%20%20-%2016%20%3D%200)
![( {a}^{2} - 8)( {a}^{2} + 2) = 0](https://tex.z-dn.net/?f=%28%20%7Ba%7D%5E%7B2%7D%20%20-%208%29%28%20%7Ba%7D%5E%7B2%7D%20%20%2B%202%29%20%3D%200)
![{a}^{2} = 8](https://tex.z-dn.net/?f=%20%7Ba%7D%5E%7B2%7D%20%20%20%3D%208)
![a = 2 \sqrt{2}](https://tex.z-dn.net/?f=%20a%20%3D%202%20%5Csqrt%7B2%7D%20)
![b = \frac{4}{2 \sqrt{2} } = \sqrt{2}](https://tex.z-dn.net/?f=b%20%3D%20%20%5Cfrac%7B4%7D%7B2%20%5Csqrt%7B2%7D%20%7D%20%3D%20%20%5Csqrt%7B2%7D%20%20)