find the multiplicative inverse of -4+3i?

Answer 1

let mult. inverse be a + bi
(- 4 + 3i) (a + b i) = 1
-4a - 4 b i + 3a i - 3b = 1
(- 4a - 3b) + i (3a - 4b) = 1

- 4a - 3b = 1
3a - 4b = 0

-12a - 9b = 3
12a - 16 b = 0-------ADD
- 25 b = 3
b = - 3 / 25

3a + 12/25 = 0
3a = - 12/25
a = - 4 / 25

-4/25 - 3/25 i is required inverse

Answer 2

Multiplicative inverse of a quantity x is a million/x So for -4+3i the multiplicative inverse is a million/(-4+3i) We multiply the two numerator and denominator via (-4-3i) to make the denominator a real quantity hence it turns into (a million/(-4+3i)) *(-4-3i/-4-3i) =(-4-3i)/25 =-4/25 -(3/25)i'm hoping that helps

Answer 3

Isn't that 1/(-4+3i)? To put it in standard form, the trick is to multiply and divide by the complex conjugate, so the denominator will be real:

1/(-4+3i) (-4-3i)/(-4-3i) = (-4-3i)/25.

Answer 4

do you mean 1/(-4+3i)?

(-4-3i)/((-4+3i)(-4-3i)

(-4-3i)/25