Complex numbers question2 Watch

SeekerOfKnowledge
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#1
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#1
fine real numbers a and b with a>0 such that

i) (a+bj)^2 = 21+20j

ii) (a+bj)^2 =j
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Glutamic Acid
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#2
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Lol, "bj". Expand (a + bj)^2 =
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a^2 - b^2 + 2jab


then compare real and imaginary parts; solving simultaneous equations.
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SeekerOfKnowledge
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(Original post by Glutamic Acid)
Lol, "bj". Expand (a + bj)^2 =
Spoiler:
Show
a^2 - b^2 + 2jab


then compare real and imaginary parts; solving simultaneous equations.
lol

okay so after i expand what do i do?
put the imaginary to one side and real to the other
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Glutamic Acid
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#4
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(Original post by SeekerOfKnowledge)
lol

okay so after i expand what do i do?
put the imaginary to one side and real to the other
Not as such. Two complex numbers are equivalent if their real parts are equivalent and their imaginary parts are equivalent.

So: (a + bj)^2 = 21 + 20j
a^2 - b^2 + 2jab = 21 + 20j; now, compare the real part from each side:
a^2 - b^2 = 21.
And the imaginary part:
2ab = 20.
Solve these equations simultaneously (substitute from the second into the first).
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