complex number

[Teen]

what is effect of multiplying any complex number by i?
can someone use a diagram  explain it.

thanks in advance:)

[BubbleWrapMan]

It rotates the number 90 degrees anticlockwise about the origin.

[Teen]

how?

[paulsterio]

i(x+yi) = ix - y = -y + ix

i.e. rotation of 90 degrees counterclockwise

[Teen]

i(x+yi) = ix - y = -y + ix

i.e. rotation of 90 degrees counterclockwise

'

i understand the expanding ....how did u know from expansion, it rotates 90 degrees anticlockwise

[paulsterio]

because x -> -y and y -> x, that's a counterclockwise rotation.

[Somye]

alternatively, use polar numbers to understand it
i = cis( pi/2)

z*i = r*1cis(theta + pi/2), which you can see is a rotation anticlockwise of 90 degrees (pi/2)

[nisha]

i(x+yi) = ix - y = -y + ix

i.e. rotation of 90 degrees counterclockwise

'

i understand the expanding ....how did u know from expansion, it rotates 90 degrees anticlockwise

draw it out.

[Teen]

alternatively, use polar numbers to understand it
i = cis( pi/2)

z*i = r*1cis(theta + pi/2), which you can see is a rotation anticlockwise of 90 degrees (pi/2)

polar form way is easier to understand.....

[Teen]

thanks everyone for ur help:)

[Jenny_2108]

alternatively, use polar numbers to understand it
i = cis( pi/2)

z*i = r*1cis(theta + pi/2), which you can see is a rotation anticlockwise of 90 degrees (pi/2)

polar form way is easier to understand.....

You should have gone to Derrick Ha's spesh lecture. He explained about it in this way