How Do You Sketch Re(iz) = 3 in Complex Number Plane?

[JC3187]

Hi guys,
So as title states, how would one sketch Re(iz) = 3? And an explanation would be splendid.

This is what I thought:

let z = a + bi
i(a+bi) = -b + ai

Therefore: Re(iz) = -b = 3

So Real axis = -3?

Or would it be Real axis = 3
Since iz is an arbitrary complex number and the real part of this arbitrary complex number is 3.

 

[Mark44]

Hi guys,
So as title states, how would one sketch Re(iz) = 3? And an explanation would be splendid.

This is what I thought:

let z = a + bi
i(a+bi) = -b + ai

Therefore: Re(iz) = -b = 3

So Real axis = -3?

What does this mean? What you have found is that if z = a + bi, the condition that Re(iz) = 3 is that z = a - 3i. What does this look like?

Or would it be Real axis = 3
Since iz is an arbitrary complex number and the real part of this arbitrary complex number is 3.

No, the imaginary part has to be -3.

 

[JC3187]

Thanks for your reply, though I am still a little confused.

Could you go through the working please?

 

[AlephZero]

You are drawing a sketch of z, not of iz.

b is the imaginary part of z.

Of course -b is also the real part of iz, but you are not drawing a sketch of iz.

 

[Mark44]

Thanks for your reply, though I am still a little confused.

What part are you confused about?

Could you go through the working please?

That's not how it works here, as listed in the rules (click Rules & Guidelines, under SITE INFO in the menu bar, especially the section titled Homework Help Guidelines).

 

[JC3187]

I think i understand, so would this be correct for the following question:

Re(z+2) = -1

-3 in the real axis?