It follows from De Moivre’s formula that zn = rn (cos n + i sin n). Thus, if we allow complex number z to describe a circle of radius r about the origin, zn will describe n complete times a circle of radius rn as z describes its circle once. We also recall that r, the modulus of z, written |z|, gives the distance of z from O, and that if z' = x' + iy', then |z – z'| is the distance between z and z'. With these preliminaries we may proceed to the proof of the theorem.
What exactly it was that pleased her in these sentences she did not know, but they conveyed weight, comfort, inevitability. Her mind strayed to Varun and his mathematical studies. She hoped that her brief words to him the day after the wedding had done him some good. She should have written to him more often to bolster his courage, but with exams coming up she had very little time for anything. It was at the insistence of Malati – who was even busier than she was – that she had gone ganjing at all.
She read the paragraph again, looking serious. ‘We also recall’ and ‘with these preliminaries’ drew her into a compact with the author of these verities and mysteries. The words were assured, and therefore reassuring: things were what they were even in this uncertain world, and she could proceed from there.
She smiled to herself now, not aware of her surroundings. Still holding the book, she looked up. And this was how a young man, who had been standing not far from her, was included, unintentionally, in her smile. He was pleasantly startled, and smiled back at her. Lata frowned at him and looked down at the page again. But she could not concentrate on it, and after a few moments, replaced it on the shelf before making her way to Poetry.
Lata, whatever she thought of love itself, liked love poetry. ‘Maud’ was one of her favourite poems. She began to flip through a volume of Tennyson.
The tall young man, who had (Lata noticed) slightly wavy black hair and very good, rather aquiline, looks, seemed to be as interested in poetry as in mathematics, because a few minutes later Lata was aware that he had shifted his attention to the poetry shelves, and was glancing through the anthologies. Lata felt that his eyes were on her from time to time. This annoyed her and she did not look up. When, despite herself, she did, she noticed him innocently immersed in his reading. She could not resist glancing at the cover of his book. It was a Penguin: Contemporary Verse. He now looked up, and the tables were turned. Before she could glance down again, he said: ‘It’s unusual for someone to be interested in both poetry and mathematics.’
‘Is that so?’ said Lata severely.
‘Courant and Robbins – it’s an excellent work.’
‘Oh?’ said Lata. Then, realizing that the young man was referring to the mathematics book she had picked randomly off the shelf, she said, ‘Is it?’ by way of closure.
But the young man was eager to continue the conversation.
‘My father says so,’ he went on. ‘Not as a text but as a broad introduction to various, well, facets of the subject. He teaches maths at the university.’
Lata looked around to see if Malati was listening. But Malati was intent on her browsing in the front of the shop. Nor was anyone else eavesdropping; the shop was not busy at this time of year – or this time of day.
‘Actually, I’m not interested in mathematics,’ said Lata with an air of finality. The young man looked a littledowncast before he rallied and confided, genially: ‘You know, nor am I. I’m a history student myself.’
Lata was amazed at his determination and, looking straight at him, said, ‘I must go now. My friend is waiting for me.’ Even as she was saying this, however, she could not help noticing how sensitive, even vulnerable, this wavy-haired young man looked. This appeared to contradict his determined, bold behaviour in speaking to an unknown, unintroduced, girl in a bookshop.
‘I’m sorry, I suppose I‘ve been disturbing you?’ he apologized, as if reading her thoughts.
‘No,’ said Lata. She was about to go to the front of the shop when he added quickly, with a nervous smile, ‘In that case, may I ask you your name?’
‘Lata,’ said Lata shortly, though she didn’t see the logic of ‘in that case’.
‘Aren’t you going to ask me mine?’ asked the young man, his smile broadening amiably.
‘No,’ said Lata, quite kindly, and rejoined Malati, who had a couple of paperback novels in her hand.
‘Who’s he?’ whispered Malati conspiratorially.
‘Just someone,’ said Lata, glancing back a bit anxiously. ‘I don’t know. He just came up to me and began a conversation. Hurry up. Let’s go. I’m feeling hungry. And thirsty. It’s hot in here.’