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    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.

    Finding complex roots of quadratics

    AHL HL 1.12

    When a quadratic

    ax2+bx+c=0

    has

    Δ=b2−4ac<0,

    it has no real roots since the square root in

    x=2a−b±√b2−4ac​​

    is not a real number. Instead, the square root will give an imaginary number, making the roots complex.


    Example

    Find the roots of z2−2z+5=0.


    z  ​=22±√22−4⋅5​​ =22±√−16​​=1±2i​

    Finding complex roots of quadratics

    AHL HL 1.12

    When a quadratic

    ax2+bx+c=0

    has

    Δ=b2−4ac<0,

    it has no real roots since the square root in

    x=2a−b±√b2−4ac​​

    is not a real number. Instead, the square root will give an imaginary number, making the roots complex.


    Example

    Find the roots of z2−2z+5=0.


    z  ​=22±√22−4⋅5​​ =22±√−16​​=1±2i​
    Cartesian formPolar formDe Moivre