0
$\begingroup$

Find a connection how the real part of z depends on the imaginary part, if the following two conditions for the complex number z apply:

  1. |z|=k, where k is a real number.

  2. The real part and the imaginary part of z are positive?

This is what I think: If the complex number z is z=a+ib then the absolute value is |z|=sqrt(a^2+b^2)=k

If a and b or a or b were negative, the absolute value would still be positive.

Am I anywhere near the answer?

Appreciate your help.

$\endgroup$
0
$\begingroup$

You're almost there: \begin{align} & \sqrt{a^2+b^2} = k \\[10pt] & a^2+b^2 = k^2 \\[10pt] & a^2 = k^2 - b^2 \\[10pt] & a = \sqrt{k^2 - b^2} \end{align} and we don't need to say $\text{“}{\pm}\text{''}$ because we know $a\ge0.$

$\endgroup$
  • $\begingroup$ Thank you that helped a lot $\endgroup$ – VitaminK Oct 20 at 19:26

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.