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Express the following complex numbers in Cartesian form, given their real (x) and imaginary (y) parts:

Mathematics

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Answers

4 parts
i

1+5i

ii

-2-i

iii

10+12i10+\frac{1}{2}i

iv

3+7i

Step-by-step solution

4 steps

The Cartesian form of a complex number is x+yix+yi, where xx is the real part and yy is the imaginary part.

Part i· 1 step

Given x=1x=1 and y=5y=5.

  1. Substitute the values of xx and yy into the Cartesian form.

    z=x+yiz = x+yi z=1+5iz = 1+5i

    The Cartesian form is 1+5i\boxed{1+5i}.

Part ii-2-i

Given x=−2x=-2 and y=−1y=-1.

  1. Substitute the values of xx and yy into the Cartesian form.

    z=x+yiz = x+yi z=−2+(−1)iz = -2+(-1)i z=−2−iz = -2-i

    The Cartesian form is −2−i\boxed{-2-i}.

Part iii

10+12i10+\frac{1}{2}i

Given x=10x=10 and y=12y=\frac{1}{2}.

  1. Substitute the values of xx and yy into the Cartesian form.

    z=x+yiz = x+yi z=10+12iz = 10+\frac{1}{2}i

    The Cartesian form is 10+12i\boxed{10+\frac{1}{2}i}.

Part iv3+7i

Given x=3x=3 and y=7y=7.

  1. Substitute the values of xx and yy into the Cartesian form.

    z=x+yiz = x+yi z=3+7iz = 3+7i

    The Cartesian form is 3+7i\boxed{3+7i}.

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