Question 40:
- 3i + 2i/ 1 + 4i
Solution your input: Simplify is 9i
Polar Form: For a complex number a + bi, polar form is given by
r(COS(0) + i SIN(0)), where r = sqrt (a)^2 + (b)^2
0 = atan (b/a
We have that a = 0 and b = 9
Thus r = sqrt (0)^2 + (9)^2 = 9
Also, 0 = atan (9/0) = pie/2
Therefore, 9i = 9 COS (pie/2) + 9i SIN (pie/2)
Inverse:
The inverse of 9i is 1/9i
Multiply and divide by i (Keep in mind that i^2 = - 1)
(i/9i) = ( - i/9)
This means that 1/9 = - i/9
Conjugate:
The conjugate of a + ib is a - ib
the conjugate of 9i is - 9i
Modulus:
The modulus of a + ib is sqrt a^2 + b^2 the modulus of 9i is 9
Answer: 9i = 9i = 9.0i
The polar form of 9i is 9i
the inverse of 9i is i/9i = - i/9 ~~ - 0.11111111111111 i
The conjugate of 9i is - 9i = - 9.0i
The modulus of 9i is 9
Question 39).
(x + 2)^3 = 0
Hope this helps!!!!! ( Question 40) 9i
