Argand plane and polar form
General · Mathematics
Study notes
Q: Write 1+i in polar form. Multiply (1+i) by i geometrically. r = √2, θ = 45° = π/4: z = √2(cos π/4 + i sin π/4). i = (1, π/2). Product: r = √2×1 = √2, θ = π/4+π/2 = 3π/4. √2(cos 3π/4 + i sin 3π/4) = -1+i ✓ (matches (1+i)i = i+i² = -1+i!). (Multiply: rotate + scale!)