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Published byJocelyn Lillie Modified over 2 years ago

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i= -1 i 2 = -1

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a+b i Real Imaginary part part

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If b0 then a+bi is a complex number called an imaginary number If b=0 then a+bi is a real number If a=0 then bi is a pure imaginary number

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-4 + 6i 2i = 0+2i 3=3+0i

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Adding (a+bi)-(c+di)=(a+c)-(b+d)i (a+bi)+(c+di)=(a+c)+(b+d)i Subtracting (5-11i)+(7+4i) (5-2i)+(3+3i) (-5+i)-(-11-6i) (2+6i)-(12-i)

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Use the distributive property and FOIL method After completing the multiplication replace i 2 with -1 4i(3-5i) (7-3i)(-2-5i)

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For the complex conjugate a+bi, its complex conjugate is a-bi. The multiplication of complex conjugates results in a real number. (a+bi)(a-bi)=a 2 +b 2 (a-bi)(a+bi)=a 2 =b 2 The goal of the division procedure is to obtain a real number in the denominator. Example 7+4i 2-5i

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The square root of 4i and-4i both result in -16. In the complex number system, - 16 has two square rolls, we use 4i as the principal square root.

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Section 8.7 Complex Numbers. Overview In previous sections, it was not possible to find the square root of a negative number using real numbers: is not.

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