Answer:
see explanation
Step-by-step explanation:
the sum to n terms of an arithmetic sequence is
= 
[2a + (n - 1)d ]
where d is the common difference and a is the first term
here d = 9 - 7 = 7 - 5 = 2 and a = 5, hence
= [(2 × 5) + 2(n - 1) ]
= (10 + 2n - 2)
= (2n + 8)
= n² + 4n
When sum = 165, then
n² + 4n = 165 ← rearrange into standard form
n² + 4n - 165 = 0 ← in standard form
(n + 15)(n - 11) = 0 ← in factored form
equate each factor to zero and solve for n
n + 15 = 0 ⇒ n = - 15
n - 11 = 0 ⇒ n = 11
but n > 0 ⇒ n = 11
Answer:
1. Complex number.
2. Imaginary part of a complex number.
3. Real part of a complex number.
4. i
5. Multiplicative inverse.
6. Imaginary number.
7. Complex conjugate.
Step-by-step explanation:
1. <u><em>Complex number:</em></u> is the sum of a real number and an imaginary number: a + bi, where a is a real number and b is the imaginary part.
2. <u><em>Imaginary part of a complex number</em></u>: the part of a complex that is multiplied by i; so, the imaginary part of the complex number a + bi is b; the imaginary part of a complex number is a real number.
3. <em><u>Real part of a complex number</u></em>: the part of a complex that is not multiplied by i. So, the real part of the complex number a + bi is a; the real part of a complex number is a real number.
4. <u><em>i:</em></u> a number defined with the property that 12 = -1.
5. <em><u>Multiplicative inverse</u></em>: the inverse of a complex number a + bi is a complex number c + di such that the product of these two numbers equals 1.
6. <em><u>Imaginary number</u></em>: any nonzero multiple of i; this is the same as the square root of any negative real number.
7. <em><u>Complex conjugate</u></em>: the conjugate of a complex number has the opposite imaginary part. So, the conjugate of a + bi is a - bi. Likewise, the conjugate of a - bi is a + bi. So, complex conjugates always occur in pairs.
I think the answer is x times 2 - 61
