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P4 Complex Numbers
We have just started AS Further Maths, and have learnt the entire, complex number topic.
Nowthen, today,, we were given 3 question from P4 to attempt,. I struggled through 2 and am badly stuck on number 3.
Given that,
z - 2
------ = Ti (where T is real)
z + 3i
Show that
z = (2 - 3T)(1 + Ti) / 1 + T²
Please help.
Thanks,
Nowthen, today,, we were given 3 question from P4 to attempt,. I struggled through 2 and am badly stuck on number 3.
Given that,
z - 2
------ = Ti (where T is real)
z + 3i
Show that
z = (2 - 3T)(1 + Ti) / 1 + T²
Please help.
Thanks,
Vazzyb
We have just started AS Further Maths, and have learnt the entire, complex number topic.
Nowthen, today,, we were given 3 question from P4 to attempt,. I struggled through 2 and am badly stuck on number 3.
Given that,
z - 2
------ = Ti (where T is real)
z + 3i
Show that
z = (2 - 3T)(1 + Ti) / 1 + T²
Please help.
Thanks,
Nowthen, today,, we were given 3 question from P4 to attempt,. I struggled through 2 and am badly stuck on number 3.
Given that,
z - 2
------ = Ti (where T is real)
z + 3i
Show that
z = (2 - 3T)(1 + Ti) / 1 + T²
Please help.
Thanks,
z-2 = Ti(z+3i) = Tzi - 3T
=> 3T - 2 = z(Ti-1)
=> 2-3T = z(1-Ti)
=> (1+Ti)(2-3T) = z(1-Ti)(1+Ti) = z[1 -Ti+Ti +T²]
=> (2-3T)(1+Ti)/(1+T²) =z as required
went a bit around the houses there >.<
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