Hi guys,
I'm asked to write the number 5/i in the a+bi form. The format is such that I can only enter the values of a and b in the computer. I'm not sure what I should write. Can anyone help me please?
Thanks a lot!
Egoyan
Hi guys,
I'm asked to write the number 5/i in the a+bi form. The format is such that I can only enter the values of a and b in the computer. I'm not sure what I should write. Can anyone help me please?
Thanks a lot!
Egoyan
More generally, a complex number, a+ bi, multiplied by its "complex conjugate", a- bi, gives a non-negative real number: $\displaystyle (a+ bi)(a- bi)= a^2+ abi - abi- b^2i^2= a^2+ b^2= |a|$. In particular, you can make denominator or a fraction a real number by multiplying the numerator and denominator by the complex conjugate of the denominator:
$\displaystyle \frac{a+ bi}{c+ di}= \frac{a+ bi}{c+ di}\frac{c- di}{c- di}= \frac{(ac+ bd)+ i(bc- ad)}{c^2+ d^2}= \frac{ac+ bd}{c^2+ d^2}+ \frac{bc- ad}{c^2+ d^2}i$.