2/i = -2i Complex numbers?

Question

Why does the above equation hold? i in this case represents the imaginary number sqr root of -1.

I don't undertand, Can anyone pls teach me Thanks a lot

Answer 1

Its simple
2/i = 2/i
= 2/i * (i/i)
= (2*i) / (i*i)
=(2*i) / (i^2)
= 2i / (-1)
2/i= -2i

Answer 2

.
2 / i = - 2 i
2 = - 2 i x i
2 = - 2 i^2
1 = - i^2
-1 = i^2
so, i^2 = -1

Answer 3

Since i is actually a radical, i.e. sq rt of -1, then what needs to be done is to rationalize the denominator, that is multiply the denominator by itself to clear out the radical. But, in order not to change the value of the entire expression, the numerator must be multiplied by the same number. So, what you are actually doing is multiplying the whole expression by 1, and changing its form in the process.

2/i = 2 / sq rt (-1) = 2 [sq rt (-1)] / [sq rt (-1)] = 2 [sq rt (-1)] / -1 = -2 i

A word of explanation is needed for the last step. Recall that dividing one number by another is the same thing as multiplying the number in the numerator by the reciprocal of the denominator. So, when we divide a number by -1, we are actually multiplying the numerator by 1/-1 = -1. That's how the negative sign is introduced into the numerator.

Answer 4

Just like for trigonometric identities, the way to prove this to be true is to start with one side and make it equal to the other side.

2/i = -2i

Let's start with the left hand side (LHS).

LHS = 2/i

Multiply numerator and denominator by i, to get

LHS = 2i/(i^2)

Note that by definition, i^2 = -1, so

LHS = 2i/(-1)

Any number divided by -1 is negated.

LHS = -2i = RHS

Answer 5

hey! that is the answer. (3+2i)(3-2i) --> Write the concern. 9+6i-6i-4i^2 --> Use FOIL. 9-4i^2 --> Cancel out the 6i words. 9-4(-a million) --> keep in mind that i^2=-a million. 9+4 --> Multiply -4 and -a million. thirteen upload 9 and four. So the answer is thirteen. desire it facilitates!

Answer 6

2/i = -2i

Multiply both sides by i

2 = -2i²

As you said, i² = -1

So 2 = -2 * -1

2 = 2

Answer 7

-1 = i^2 (property of i)
2 = - 2 i x i
hence
2/i = -2 i

Answer 8

i² = 1
2/i = -2i
2 = -2i*i
2 = -2i²
2 = -2.-1
2 = 2
::

Answer 9

if you multiply both sides by i you get 2= -2*(i^2) but i^2 =-1
so 2=2(verified)

Answer 10

(2/i)=(2/i)*(-1)/(-1)
=(2*i^2)/-i
= 2*i*i/-i
=-2i