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This module provides practice problems related to complex numbers.

( 3 + 7 i ) ( 4 + 7 i ) =

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( 5 3 i ) + ( 5 3 i ) =

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( 5 3 i ) ( 2 + 0 i ) =

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What is the complex conjugate of ( 5 3 i ) ?

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What do you get when you multiply ( 5 3 i ) by its complex conjugate?

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What is the complex conjugate of 7?

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What do you get when you multiply 7 by its complex conjugate?

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What is the complex conjugate of 2 i ?

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What do you get when you multiply 2 i by its complex conjugate?

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What is the complex conjugate of ( a + b i ) ?

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What do you get when you multiply ( a + b i ) by its complex conjugate?

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I’m thinking of a complex number z . When I multiply it by its complex conjugate (designated as z * ) the answer is 25.

  • A

    What might z be?
  • B

    Test it, and make sure it works—that is, that ( z ) ( z * ) = 25 !
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I’m thinking of a different complex number z . When I multiply it by its complex conjugate, the answer is 3 + 2 i .

  • A

    What might z be?
  • B

    Test it, and make sure it works—that is, that ( z ) ( z * ) = 3 + 2 i !
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Solve for x and y : x 2 + 2 x 2 i + 4 y + 40 y i = 7 2 i

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Finally, a bit more exercise with rational expressions. We’re going to take one problem and solve it two different ways. The problem is 3 2 + i 7i 3 + 4i size 12{ { {3} over {2+i} } - { {7i} over {3+4i} } } {} . The final answer, of course, must be in the form a + b i .

  • A

    Here is one way to solve it: the common denominator is ( 2 + i ) ( 3 + 4 i ) . Put both fractions over the common denominator and combine them. Then, take the resulting fraction, and simplify it into a + b i form.
  • B

    Here is a completely different way to solve the same problem. Take the two fractions we are subtracting and simplify them both into a + b i form, and then subtract.
  • C

    Did you get the same answer? (If not, something went wrong…) Which way was easier?
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Source:  OpenStax, Advanced algebra ii: activities and homework. OpenStax CNX. Sep 15, 2009 Download for free at http://cnx.org/content/col10686/1.5
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