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In the equation above, a and b are constants. If . what is the value of a?
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If = then (a+bi) is the number reciprocal to :
a + bi = = ,
and all we need to do is to rid of the denominator in the fraction .
For it, multiply the fraction by . Since the last fraction is 1, multiplication will not change our number .
People also say "let us multiply the numerator and the denominator of an original fraction by (3-i) ").
So, we have
= =
and since = -1,
= = = 0.5 - 0.5*i.
Thus we got a + bi = 0.5 - 0.5*i.
It implies a = 0.5, b = -0.5. The problem is solved. Your answer is: a = 0.5, b = -0.5.
On complex numbers, you have these lessons
- Complex numbers and arithmetic operations on them
- Complex plane
- Addition and subtraction of complex numbers in complex plane
- Multiplication and division of complex numbers in complex plane
- Raising a complex number to an integer power
- How to take a root of a complex number
- Solution of the quadratic equation with real coefficients on complex domain
- How to take a square root of a complex number
- Solution of the quadratic equation with complex coefficients on complex domain
in this site.