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
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.
The video will automatically pause when it reaches a problem.
AHL HL 1.12
If a=0, then tan(argz)=ab is undefined. But we recall that tanθ is undefined for θ=2π,23π… So when a=0 we have
This can be seen on the complex diagram by remembering that bi lies on the yi axis:
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Example
Find the argument of z=−3i.
We have z=0−3i, so z is purely imaginary and lies along the y-axis. Since −3<0, the argument of z is argz=23π.
AHL HL 1.12
If a=0, then tan(argz)=ab is undefined. But we recall that tanθ is undefined for θ=2π,23π… So when a=0 we have
This can be seen on the complex diagram by remembering that bi lies on the yi axis:
Powered by Desmos
Example
Find the argument of z=−3i.
We have z=0−3i, so z is purely imaginary and lies along the y-axis. Since −3<0, the argument of z is argz=23π.