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Complex Numbers (Foundations)

Core skills for this exam family.

Phase 2 · JEE

FoundationsStandardAdvanced

Complex Numbers: core idea

∣a+bi∣=a2+b2|a+bi|=\sqrt{a^2+b^2}.

Example problem: hint and answer

i2i^2?

Hint: Definition. Answer: -1.

Practice (9 problems — type your answers)

  • 1. i3i^3?

  • 2. ∣3+4i∣|3+4i|?

  • 3. Conjugate of 2−3i2-3i: imaginary part?

  • 4. (1+i)+(2−i)(1+i)+(2-i): real part?

  • 5. i(1+i)i(1+i): real part?

  • 6. Real part of 3−2i3-2i?

  • 7. arg⁡(1+i)\arg(1+i) in degrees?

  • 8. Solve z2+1=0z^2+1=0: positive imaginary root as bibi with b=b=?

  • 9. 1/i1/i?

Complex Numbers Practice Problems — Foundations