WEBVTT
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Find the real values of π₯ and π¦ that satisfy the equation two π₯ minus five plus π¦π is equal to negative three take away five π.
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Well our question has given us two complex numbers, one on either side of the equation.
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And in complex numbers, theyβre made up of a real part which is this bit here, and an imaginary part which in this case this bit here.
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Now the real components of these must be equal, because, well, overall numbers are equal.
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And the imaginary parts must be equal.
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So we can actually create two equations.
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If the real parts are equal, then two π₯ minus five must be equal to negative three.
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Then if I add five to both sides of that equation, two π₯ minus five on the left-hand side is just two π₯.
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And negative three plus five on the right-hand side is positive two.
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Now if I divide both sides by two, I get π₯ is equal to one.
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Now also the imaginary parts are equal, so π¦ must be equal to negative five.
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This part of this number is equal to this part of this number.
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So the answer then π₯ equals one and π¦ equals negative five.