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  • Perplex
    IB Math AIHL
    /
    Complex Numbers
    /

    Video

    Video Reviews

    Watch comprehensive video reviews for most units, designed for final exam preparation. Each video includes integrated problems you can solve alongside detailed solutions.

    Not your average video:

    Interactive Problems: Solve problems alongside the video with step-by-step guidance and detailed solutions.

    Exam Preparation: Complete unit reviews designed for final exam preparation with all key concepts covered systematically.

    Expert Teaching: High-quality instruction from Perplex co-founder James Mullen with clear explanations, worked examples, and exam tips.

    Not your average video:

    Interactive Problems: Solve problems alongside the video with step-by-step guidance and detailed solutions.

    Exam Preparation: Complete unit reviews designed for final exam preparation with all key concepts covered systematically.

    Expert Teaching: High-quality instruction from Perplex co-founder James Mullen with clear explanations, worked examples, and exam tips.

    Complex Numbers

    Video Reviews

    Watch comprehensive video reviews for Complex Numbers, designed for final exam preparation. Each video includes integrated problems you can solve alongside detailed solutions.

    Not your average video:

    Interactive Problems: Solve problems alongside the video with step-by-step guidance and detailed solutions.

    Exam Preparation: Complete unit reviews designed for final exam preparation with all key concepts covered systematically.

    Expert Teaching: High-quality instruction from Perplex co-founder James Mullen with clear explanations, worked examples, and exam tips.

    Not your average video:

    Interactive Problems: Solve problems alongside the video with step-by-step guidance and detailed solutions.

    Exam Preparation: Complete unit reviews designed for final exam preparation with all key concepts covered systematically.

    Expert Teaching: High-quality instruction from Perplex co-founder James Mullen with clear explanations, worked examples, and exam tips.

    Cartesian formPolar formDe Moivre

    The video will automatically pause when it reaches a problem.

    Solving complex equations

    AHL HL 1.12

    By remembering that a complex number z takes the form a+bi, we can solve complex equations such as

    z+2i=3iz∗−2


    ⇒a+bi+2ia+(b+2)i​=3i(a−bi)−2=3ai+(3b−2)​


    Now we equate the real and imaginary parts of both sides:

    {a=3b−2b+2=3a​

    Substituting a=3b−2 into b+2=3a:

    b+2=9b−6⇒8b=8⇒b=1

    and therefore a=1.


    So z=1+i.

    Solving complex equations

    AHL HL 1.12

    By remembering that a complex number z takes the form a+bi, we can solve complex equations such as

    z+2i=3iz∗−2


    ⇒a+bi+2ia+(b+2)i​=3i(a−bi)−2=3ai+(3b−2)​


    Now we equate the real and imaginary parts of both sides:

    {a=3b−2b+2=3a​

    Substituting a=3b−2 into b+2=3a:

    b+2=9b−6⇒8b=8⇒b=1

    and therefore a=1.


    So z=1+i.

    Cartesian formPolar formDe Moivre